Explanation Procedure used: To find x and y components of a vector: 1. Place the vector A such that θ is in standard position. 2. Calculate A x and A y from A x = A cos θ and A y = A sin θ . Use the reference angle if the direction of the component is noted. 3. Check the components to see if each is in the correct direction and has a magnitude that is proper for the reference angle. Adding vectors by components: 1. Add the x -component of the given vectors to obtain R x . 2. Add the y -component of the given vectors to obtain R y . 3. Find the magnitude of the resultant R . Use the equation R = R x 2 + R y 2 . 4. Find the standard-position angle θ for the resultant R . Find the reference angle θ r e f for the resultant R by using the equation θ r e f = tan − 1 | R y | | R x | . Then, use the reference angle and the quadrant of R to determine the standard position angle θ . Calculation: In example 4, the vector U = 405 is directed at an angle θ U = 235 ° and V = 210 is directed at an angle θ V = 110 ° . Sketch the figure of the corresponding vectors as shown below in Figure 1. From Figure 1, it is observed that the vector U = 405 is directed at an angle θ U = 235 ° and V = 210 is directed at an angle θ V = 110 ° . Let the resultant vector is represented as R . Then, the x component of the resultant vector R is, R x = U x + V x = U cos θ U + V cos θ V = 405 cos 235 ° + 210 cos 110 ° = ( − 232.30 ) + ( − 71.82 ) ≈ − 304.12 Similarly, the y component of the resultant vector R is, R y = U y + V y = U sin θ U + V sin θ V = 405 sin 235 ° + 210 sin 110 ° = ( − 331

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 9.3, Problem 3PE

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The resultant vector R of the vectors U and V in example 4.

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Chapter 9.3, Problem 2PE

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Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 9.1 - For the vectors in Example 2, show that R = B + C...Ch. 9.1 - Prob. 2PE Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E

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