WebLearn how to write a vector in component form given two points and also how to determine the magnitude of a vector given in component form. These cookies track visitors across websites and collect information to provide customized ads. And then, the second Vector AB is being constructed of this X, this vector that goes Practice. To find the resultant of two vectors in component form just add the x components of each and the y components of each. WebAs we know that the resultant vector is given as: R = OA + OB +OC R = 5 + 10 + 15 R = 30N Example 2 Find out the resultant vector of the given Get help from expert tutors If you're struggling with a particular subject, get help from one of our expert tutors. How do you calculate the component form of a vector in 3D (x,y,z)? A: The length of a vector x=abc is given by the equation; ||x||=a2+b2+c2. Having a good knowledge of vector operations is important as in physics we have to deal with numerous vector quantities. The direction of the resultant force is in the same direction as the larger force. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Direct link to bheeni's post when sal sir says "negati, Posted 4 years ago. tan = Ax Ay tan = A x A y. or, = tan1(Ax Ay) = tan 1 ( A x A y) This is how you identify the direction angle of a vector in a plane when you have knowledge of x and y components of a vector. WebTo find the magnitude of a vector from its components, we take the square root of the sum of the components' squares (this is a direct result of the Pythagorean theorem): || (a,b)||=\sqrt {a^2+b^2} (a,b) = a2 + b2 For example, the magnitude of (3,4) (3,4) is \sqrt {3^2+4^2}=\sqrt {25}=5 32 +42 = 25 = 5. Practice. The component form of a vector is the ordered pair that describes the changes in the x- and y-values. Let the angle between the vector and its x -component be . Here a, b, c are also termed as rectangular components. If you're seeing this message, it means we're having trouble loading external resources on our website. about the components, at least in this context, they're just talking about The head to tail method is way to find the resultant vector. This section provide citations and links to suggested readings, courses, 7.1 finding rational solutions of polynomial equations practice and problem solving a/b. Point of Intersection of Two Lines Formula. Two vectors are shown below: #color(red)(vec(OA) and vec(OB)# We will also be using these vectors in our example later. You can always count on us for help, 24 hours a day, 7 days a week. There are a two different ways to calculate the resultant vector. In mathematics, we often heard about the two terms scalar and vector. How many whole numbers are there between 1 and 100? WebVector Addition. The head to tail method is way to find the resultant vector. Library: Component form of a vector with initial point and terminal point. A resultant vector is the of two or more vectors. To solve a word question, you need to first understand what is being asked, and then identify the key words and phrases that will help you solve the problem. The vector component in the y-axis, is approximately 22.6. The cookie is used to store the user consent for the cookies in the category "Other. A vector is equal to its terminal point minus its initial point. This formula has various applications in Engineering & Physics. This website uses cookies to improve your experience while you navigate through the website. This cookie is set by GDPR Cookie Consent plugin. Necessary cookies are absolutely essential for the website to function properly. The angle labeled as theta () is the angle between the resultant vector and the west axis. In this case, the direction is left and down. In the graph above x1=0, y1=0 and x2=2, y2=5. The reason an arrow is used is because a vector uses magnitude, the amount something moves, or the speed with which it moves, and direction. Direct link to mesmerjessica's post How do you calculate the , Posted 3 years ago. The component form of a vector is the ordered pair that describes the changes in the x- and y-values. Direct link to loumast17's post If you have all three coo, Posted 3 years ago. what our change in X is, and like always, I encourage I think i missed something along the way. And then point B, its coordinates are, let's see its X coordinate is (-7,-8). We are given the points A=(1,3), B=(-4,5), C=(-2,10), D=(0,1). This cookie is set by GDPR Cookie Consent plugin. Given two point vectors with one representing the initial point and the other representing the terminal point. To find the direction of the vector when its components Ax A x and Ay A y are given we use. WebVector Calculator. We also use third-party cookies that help us analyze and understand how you use this website. The resultant vector from the given vectors is 0i-9j-2k, Question 4: Find the resultant vector for the vectors 9i+2j-3k and i-3j+2k, Given two vectors are a=9i+2j-3k and b=i-3j+2k, The resultant vector from the given vectors is 8i+5j-5k. This cookie is set by GDPR Cookie Consent plugin. WebTo find the magnitude of a vector from its components, we take the square root of the sum of the components' squares (this is a direct result of the Pythagorean theorem): || (a,b)||=\sqrt {a^2+b^2} (a,b) = a2 + b2 For example, the magnitude of (3,4) (3,4) is \sqrt {3^2+4^2}=\sqrt {25}=5 32 +42 = 25 = 5. "We started at negative four." The angle labeled as theta () is the angle between the resultant vector and the west axis. How do you know what direction to move the arrows, right or left? What are the benefits of board and batten siding? The cookies is used to store the user consent for the cookies in the category "Necessary". To find out how fast the ball is traveling toward the table edge, you need not the balls total speed but the x component of the balls velocity. What's the point of knowing the components? WebAdvanced Math Solutions Vector Calculator, Simple Vector Arithmetic Vectors are used to represent anything that has a direction and magnitude, length. The head to tail method is way to find the resultant vector. The angle labeled as theta () is the angle between the resultant vector and the west axis. Wouldn't the change in x and y be ( 11, 12 ) ? ; It is represented by an arrow (head) and the tail which indicates the direction.The length is proportional to the quantity's magnitude. The component form of a vector is the ordered pair that describes the changes in the x- and y-values. WebA: The vector from one point to other is the difference between similar coordinates of two points. To move to the left on the x-axis and down on the y-axis would be to move down in numbers, thus negative. Web1) The arrow over the top of AB indicates that the vector starts at A and terminates at B; and 2) If you look at the diagram, it'll show that the arrow does, in fact, "point" toward the point B. This method involves properties of parallelograms but, in the end, boils down to a simple formula. vector to this blue-green, dark blue-green vector, you would get vector AB, but we'll talk more about Two vectors are equal if they have the same magnitude and direction. The vector V is broken into two components such as v x and v y. Direct link to Yousef Osama's post If vector A = 12i 16j a, Posted 3 years ago. purely in the Y direction. What is the resultant of 3 vectors? WebComponent form of a vector Mathematics High School answered Find the component form of the resultant vector.1) u = (20,-21) find -3u jazestab is waiting for your help. i.e. Direct link to Ian Pulizzotto's post A vector is equal to its , Posted 4 years ago. It is the result of adding two or more vectors together. finished at negative seven. The ordered pair that describes the changes is (x2- x1, y2- y1), in our example (2-0, 5-0) or (2,5). Components of a Vector. Posted 7 years ago. Question: Give the component form of the resultant vector in the following. The resultant vector is the vector that results from adding two or more vectors together. If the vectors are in the same direction then the resultant of the vector can be calculated by adding the vectors which are in the same direction. Now let an angle , is formed between the vector V and x-component of vector. Invest in math tutoring to support student remediation and acceleration. i'-l'f) 13 . And there's a couple of If you could just visually you to pause the video and try to work through it on your own. WebThe resulting vector formula can be used in physics, engineering and mathematics. Vector quantity has both magnitude and direction. Q: Find the length of the vector a %3D. 14. So I got this question asking: Vector AB has a terminal point (4,-7), an x component of -3 and a y component of -9. WebTo find the resultant of two vectors in component form, just add the x components of each and the y components of each. The component form of a vector is given as < x, y >, where x describes how far right or left a vector is going and y describes how far up or down a vector is going. The x component is a scalar (a number, not a vector), and you write it like this: vx. WebThese two components are supposed to form a right-angled triangle. What is the pedagogical reason for using parenthesis vector notation? This method involves properties of parallelograms but, in the end, boils down to a simple formula. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". WebVector Addition. WebComponent form of a vector Mathematics High School answered Find the component form of the resultant vector.1) u = (20,-21) find -3u jazestab is waiting for your help. Question 1: Find the resultant vector for the vectors i+2j+3k and 4i+8j+12k, Given two vectors are a=i+2j+3k and b=4i+8j+12k. What is the importance of the number system? So, this point right over here, point A, its coordinates are (4,4). Web1) The arrow over the top of AB indicates that the vector starts at A and terminates at B; and 2) If you look at the diagram, it'll show that the arrow does, in fact, "point" toward the point B. If you want to contact me, probably have some question write me email on support@onlinemschool.com. This cookie is set by GDPR Cookie Consent plugin. There are a two different ways to calculate the resultant vector. WebGiven a vectors initial point (where it starts), (x, y), and terminal point (where it ends), (x, y) the component form can be found by subtracting the coordinates of each point: < x x, y y > Learn what it means to bring Yup to your school or district Schedule Demo WebAnswer to Solved Find the component form of the resultant vector. this point right over here. Question: Give the component form of the resultant vector in the following. Now complete the summing to calculate the net force in each direction. A: The length of a vector x=abc is given by the equation; ||x||=a2+b2+c2. The component form of vector AB with A(Ax, Ay) and B(Bx, By) can be found using the following formula: Three-dimensional vectors. Given two vectors are a=2i+2j+2k and b=i+2j+3k, Also given that given two vectors are inclined at an angle =30, So the resultant vector formula for the given vectors is given by-, Magnitude of vector a (a2) = \sqrt{2^2+2^2+2^2}, Magnitude of vector b (b2) = \sqrt{1^2+2^2+3^2}, The resultant vector from the given vectors is 29.65. To try to understand what a resultant is consider the following story. So that's negative 11. letter Delta for change in X. By convention we assign three unit vectors i, j and k in the directions x, y and z respectively. Why not use matrix notation (x above y) or angle vector brackets? In the picture on the left, the black vector is the resultant of the two red vectors. The ordered pair that describes the changes is (x2- x1, y2- y1), in our example (2-0, 5-0) or (2,5). Consider a vector v. Its two components directed along the x and y-axis would be vx and vy, respectively. But opting out of some of these cookies may affect your browsing experience. Find: First, find both vectors from the initial and final points: Now find the sum of both vector by adding the components separately: Therefore, you can say that. The component form of vector AB with A(Ax, Ay, Az) and B(Bx, By, Bz) can be found using the following formula: You can input only integer numbers, decimals or fractions in this online calculator (-2.4, 5/7, ). Addition and subtraction of two vectors, Online calculator. The head to tail method is way to find the resultant vector. The angle labeled as theta () is the angle between the resultant vector and the west axis. Let vector lltll= 44mph with a direction of 240 Let vector b have a magnitude of 32 mph at a direction of 100 . You ALWAYS subtract the points. Suppose a vector V is defined in a two-dimensional plane. Luis Hoyos. How do you find the resultant vector in component form? The problem you're given will define the direction of the vector. By using our site, you The x component is a scalar (a number, not a vector), and you write it like this: vx. The component form of the resultant vector 2u - 3v = (33,10) The answer is 33 on the y-axis and 10 on the x-axis.. What is a vector? Question 5: Find the resultant of the vectors 2i+2j+2k and i+2j+3k which are inclined at an angle 30 to each other. Example 2: Find the resultant of the vectors having magnitudes of 5 units, 6 units, and are inclined to each other at an angle of 60 degrees. In the graph above x1=0, y1=0 and x2=2, y2=5. WebThe parallelogram method to calculate resultant vector. MIT OpenCourseWare is a web based publication of virtually all MIT course, This syllabus section provides the course description and information on. when sal sir says "negative 4" why he denotes to "positive 4"? Direct link to Wesley's post Around the end of the vid, Posted 7 years ago. So two vectors are in the same direction. Invest in math tutoring to support student remediation and acceleration. And then how much do we have Length of a vector, magnitude of a vector on plane, Exercises. To find out how fast the ball is traveling toward the table edge, you need not the balls total speed but the x component of the balls velocity. In my Trigonometry class, my teacher specifically said to use Chevron brackets, which are , when writing component form. You can navigate between the input fields by pressing the keys "left" and "right" on the keyboard. i'-l'f) 13 . Vectors Algebra Index. To find the magnitude of a vector from its components, we take the square root of the sum of the components' squares (this is a direct result of the Pythagorean theorem): To find the direction of a vector from its components, we take the inverse tangent of the ratio of the components: This results from using trigonometry in the right triangle formed by the vector and the, The calculator returned a negative angle, but it's common to use positive values for the direction of a vector, so we must add. When entering the force vectors into the equation, enter both the magnitude and the direction (+ or ) within the parentheses. Direct link to zzzwhking's post problem2.2 has two answer, Posted 6 years ago. Explain different types of data in statistics, Difference between an Arithmetic Sequence and a Geometric Sequence. Convert from polar coordinates to cartesian coordinates. In the picture on the left, the black vector is the resultant of the two red vectors. Example 2: Find the resultant of the vectors having magnitudes of 5 units, 6 units, and are inclined to each other at an angle of 60 degrees. direction. A Vector is defined as a quantity with both magnitude and direction. WebThe parallelogram method to calculate resultant vector. Direct link to Sathvik Suresh's post So I got this question as, Posted 6 years ago. Question 6: Find the resultant of the vector having magnitude 2, 4 which is inclined at 45. The three resultant vector formulas are: R = A + B. R = A - B. R2 = A2 + B2 + 2ABCos . Write the component form and find the direction of the resultant. ; It is represented by an arrow (head) and the tail which indicates the direction.The length is proportional to the quantity's magnitude. Vectors cannot be added by usual algebraic rules. Components of a Vector. The interaction of several force vectors on a body is an example of the resultant vector, and the resulting vector is obtained using this formula. Dot product of two vectors in space, Exercises. By clicking Accept All, you consent to the use of ALL the cookies. These cookies will be stored in your browser only with your consent. Two vectors are equal if they have the same magnitude and direction. These cookies ensure basic functionalities and security features of the website, anonymously. A vector has both magnitude (which is its length) and direction (which is its angle). ways you could compute that. Yep, you use the components and trigonometry to determine the angle of the vector, and that tells you the direction. Online calculator. Direct link to Nataly Barrios Garcia's post How do you know what dire, Posted 3 years ago. Using the identical notation, just makes the situation worse. The three resultant vector formulas are: R = A + B. R = A - B. R2 = A2 + B2 + 2ABCos . But opting out of some of these cookies may affect your browsing experience. The component form of the vector formed by the two point vectors is given by the components of the terminal point minus the corresponding components of the initial point. Direct link to khalid's post why we call the the cha, Posted 5 years ago. Vector addition, or subtraction, is just combining steps in the various directions. How do you find the resultant vector of a graph? Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. If you're struggling to clear up a math equation, try breaking it down into smaller, more manageable pieces. Step 1: Line up the head of the first vector with the tail of the second vector, which is automatic for this problem. essentially our change in X. The negative tells us that It depends on what? The net force is the vector sum of all the forces. Direct link to Jordan Cooper's post Are there situations in w, Vector components from magnitude and direction. NOTE: Answer must be typed in using the following format --including the parentheses: (#,#) u = (3, -4) v = (-5, -2) 2. 1) u = (-11, 2) b= (10,-4) 2) u = (6, 11) b = (1, -10) Find:-u- Find: -u + b 3) f= (12, 12) = (6, -12) Find: -f+ Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. Then state the magnitude and direction angle of the resultant. - [Voiceover] Find the The only real difference is that we've defined addition between vectors. If you only have the magnitude and some angle, you would actually need two angles, usually from two of the three planes. How do you write a good story in Smash Bros screening? WebHow do we use the components of two vectors to find the resultant vector by adding the two vectors ? The angle labeled as theta () is the angle between the resultant vector and the west axis. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. i'-l'f) 13 . To find the direction of the vector when its components Ax A x and Ay A y are given we use. So our change in Y, our change in Y, what's I designed this web site and wrote all the mathematical theory, online exercises, formulas and calculators. Find: First, find both vectors from the initial and final points: Now find the sum of both vector by adding the components separately: There are a two different ways to calculate the resultant vector. And I'm ending up at Y is equal to, let me do that in that other color. Consider a vector v. Its two components directed along the x and y-axis would be vx and vy, respectively. Sometimes all you need is a fresh perspective to see the answer. The three resultant vector formulas are: R = A + B. R = A - B. R2 = A2 + B2 + 2ABCos . As long as all three vectors are included with their specified magnitude and direction, the resultant will be the same. This cookie is set by GDPR Cookie Consent plugin. Learn about Vectors and Dot Products. Enter values into Magnitude and Angle or X and Y. tan = Ax Ay tan = A x A y. or, = tan1(Ax Ay) = tan 1 ( A x A y) This is how you identify the direction angle of a vector in a plane when you have knowledge of x and y components of a vector. Practice. The head to tail method is way to find the resultant vector. In the graph above x1=0, y1=0 and x2=2, y2=5. The resultant vector formula for the given vectors is given by- r = a + b = (i+2j+3k) + (4i+8j+12k) = 5i+10j+15k The resultant vector from the given vectors is 5i+10j+15k Question 2: Find the resultant vector for the vectors i-2j+5k and 2i-4j+10k Solution: Given two vectors are a=i-2j+5k and b=2i-4j+10k Review how to find a vector's magnitude and direction from its components and vice versa. Web/ 4ind a vector in component form that has a direction of256 and a magnitude of 12 ft. <12.CD 25 , 1.2 sin 5"") (-2. qo 3J -II. Direct link to jackeames's post Do you add 270 degrees to, Posted 6 years ago. In the graph above x1=0, y1=0 and x2=2, y2=5. Direct link to Anirudh Subramanian's post I've seen any questions o, Posted 7 years ago. What is the safe score in JEE Mains 2021? Vectors Algebra Index. going to be my final Y value, which is negative eight, minus my initial Y value, which is four, minus four, which is equal to negative 12. When entering the force vectors into the equation, enter both the magnitude and the direction (+ or ) within the parentheses. Direct link to Vincent Thien Pandey's post sal says negative four bu. The following list is the list of some of the common operations that are performed on vectors in the field of physics: Addition/Subtraction of two vectors. A vector is an object that has both a magnitude as wel as direction. ; WebTo find the resultant of two vectors in component form, just add the x components of each and the y components of each. And you could see that. A unit vector is simply a vector with unit magnitude. 2 What is the expression for resultant vector? WebComponents of a Vector Definition. Direct link to loumast17's post Yep, you use the componen, Posted 4 years ago. If the direction is defined by the problem as "B to A", you subtract Point A - Point B. I've seen any questions of this kind that don't provide graphs like this. In the graph above x1=0, y1=0 and x2=2, y2=5. Find the resultant vector. Analytical cookies are used to understand how visitors interact with the website. Math is my weakest subject and whenever I need help this app never fails to provide! You also have the option to opt-out of these cookies. Then I have to go down another eight, so I have to go down a total of 12. Then state the magnitude and direction angle of the resultant. WebAnswer to Solved Find the component form of the resultant vector. Adding vectors A + B + C gives the same resultant as adding vectors B + A + C or even C + B + A. The head to tail method is way to find the resultant vector. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. The head to tail method to calculate a resultant which involves lining up the head of the one vector with the tail of the other. Learn about Vectors and Dot Products. These components are then used to find the resultant vectors magnitude and direction, which is AB. WebVector Calculator. Methods for calculating a Resultant Vector: The head to tail A resultant vector is the of two or more vectors. Direct link to loumast17's post Vector addition, or subtr, Posted 6 years ago. I wonder how to calcualte the direction of a vector, which is not in the standard position. WebHow do we use the components of two vectors to find the resultant vector by adding the two vectors ? If you have all three coordinates it is super simple. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. For the situation of the three forces on the force board, the net force is the sum of force vectors A + B + C. To find the resultant of two vectors in component form, just add the x components of each and the y components of each. WebFind the component form of the resultant vector - When you try to Find the component form of the resultant vector, there are often multiple ways to approach it. that in future videos. Direct link to jwinder47's post I'm assuming you are refe, Posted 5 years ago. Let b be a vector which is in opposite direction with respect to vector a then the resultant vector r is given by-, If any vectors are inclined to each other at some angle then the resultant of these vectors can be calculated by this formula. Now let an angle , is formed between the vector V and x-component of vector. Write the component form and find the direction of the resultant. WebAnswer to Solved Find the component form of the resultant vector. Direct link to Madd Sam's post That is an effective way , Posted 6 years ago. These cookies will be stored in your browser only with your consent. Solution: Enter values into Magnitude and Angle or X and Y. The component form of a vector is the ordered pair that describes the changes in the x- and y-values. Type the coordinates of the initial and terminal points of vector; Press the button "=" and you will have a detailed step-by-step solution. Area of triangle formed by vectors, Online calculator. we decreased in X by 11. What is the probability sample space of tossing 4 coins? Can you solve for a resultant force given its components? The values a, b, c are called the scalar components of vector A, and a ^i i ^, b ^j j ^, c ^k k ^, are called the vector components. What is the resultant of 3 vectors? Do you add 270 degrees to the calculator output in the third quadrant? How do you find the component form of the resultant vector? Therefore, you can say that. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. So that right over there Two vectors are equal if they have the same magnitude and direction. Component form of a vector with initial point and terminal point on plane, Exercises. ( 2 votes) khalid 5 years ago why we call the the change in x and the change in y component of the vector ? ; The angle labeled as theta () is the angle between the resultant vector and the west axis. A: The length of a vector x=abc is given by the equation; ||x||=a2+b2+c2. Table of Content. The ordered pair that describes the changes is (x2- x1, y2- y1), in our example (2-0, 5-0) or (2,5). WebComponents of a Vector Definition. Direct link to Unpotato's post In my Trigonometry class,, Posted 5 years ago. Is there a video on questions like this. WebThe following resultant vector formula can be used here. Shouldn't the vector be -11,-12 instead of (-11,-12)? The y component of the balls velocity vector is vy. To find the resultant of two vectors in component form, just add the x components of each and the y components of each. To find the resultant of two vectors in component form, just add the x components of each and the y components of each. The angle labeled as theta () is the angle between the resultant vector and the west axis. WebThe component form of a vector is given as x, y , where x describes how far right or left a vector is going and y describes how far up or down a vector Fast answers In a world where we can get answers to our questions faster than ever before, it's important to have a source that can give us the information we need quickly and accurately. There are a two different ways to calculate the resultant vector. Find the resultant vector. Sal finds the x and y-components of a vector given its graph. left parenthesis, a, comma, b, right parenthesis, vertical bar, vertical bar, left parenthesis, a, comma, b, right parenthesis, vertical bar, vertical bar, equals, square root of, a, squared, plus, b, squared, end square root, theta, equals, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, b, divided by, a, end fraction, right parenthesis, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, b, divided by, a, end fraction, right parenthesis, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, b, divided by, a, end fraction, right parenthesis, plus, 180, degree, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, b, divided by, a, end fraction, right parenthesis, plus, 360, degree, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, left parenthesis, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, cosine, left parenthesis, theta, right parenthesis, comma, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, sine, left parenthesis, theta, right parenthesis, right parenthesis, left parenthesis, 3, comma, 4, right parenthesis, start color #11accd, start text, m, a, g, n, i, t, u, d, e, end text, end color #11accd, start color #1fab54, start text, d, i, r, e, c, t, i, o, n, end text, end color #1fab54, vertical bar, vertical bar, v, with, vector, on top, vertical bar, vertical bar, square root of, 3, squared, plus, 4, squared, end square root, equals, square root of, 25, end square root, equals, 5, u, with, vector, on top, equals, left parenthesis, 1, comma, 7, right parenthesis, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, equals, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, 4, divided by, 3, end fraction, right parenthesis, approximately equals, 53, degrees, left parenthesis, 3, comma, minus, 4, right parenthesis, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, minus, 4, divided by, 3, end fraction, right parenthesis, approximately equals, minus, 53, degrees, minus, 53, degrees, plus, 360, degrees, equals, 307, degrees, left parenthesis, minus, 3, comma, 4, right parenthesis, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, 4, divided by, minus, 3, end fraction, right parenthesis, approximately equals, minus, 53, degrees, minus, 53, degrees, plus, 180, degrees, equals, 127, degrees, u, with, vector, on top, equals, left parenthesis, 5, comma, 8, right parenthesis, 2, slash, 3, space, start text, p, i, end text, u, with, vector, on top, equals, left parenthesis, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, cosine, left parenthesis, theta, right parenthesis, comma, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, sine, left parenthesis, theta, right parenthesis, right parenthesis, start color #11accd, 2, end color #11accd, start color #1fab54, 30, degrees, end color #1fab54, left parenthesis, start color #11accd, 2, end color #11accd, cosine, left parenthesis, start color #1fab54, 30, degrees, end color #1fab54, right parenthesis, comma, start color #11accd, 2, end color #11accd, sine, left parenthesis, start color #1fab54, 30, degrees, end color #1fab54, right parenthesis, right parenthesis, equals, left parenthesis, square root of, 3, end square root, comma, 1, right parenthesis, u, with, vector, on top, approximately equals, left parenthesis, space, I think there's only one answer that fits the question.