Explanation Procedure used: To find x andy 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: The given vectors Y = 51.33 is directed at an angle θ Y = 51.33 ° and Z = 42.61 is directed at an angle θ Z = 291.77 ° Sketch the figure of the corresponding vectors as shown below in Figure 1. From Figure 1, it is observed that the resultant vector is represented as R . The x and y components of a vector Y is, Y x = Y cos θ and Y y = Y sin θ Y x = 51.33 cos 12.25 ° and Y y = 51.33 sin 12.25 ° Y x = 50.16 and Y y = 10.89 Similarly, the x and y components of a vector Z is, Z x = Z cos θ and Z y = Z sin θ Z x = 42.61 cos 291.77 ° and Z y = 42.61 sin 291.77 ° Z x = 15.80 and Z y = − 39.57 Then, the x component of the resultant vector R is, R x = Y x + Z x = 50

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Chapter 9, Problem 19RE

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The Resultant vector R and standard position angle θ by adding the components Y=51.33,θY=12.25°,Z=42.61 and θZ=291.77°.

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Chapter 9, Problem 18RE

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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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The Resultant vector R and standard position angle θ by adding the components Y = 51.33 , θ Y = 12.25 ° , Z = 42.61 and θ Z = 291.77 ° .

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The Resultant vector R and standard position angle θ by adding the components Y=51.33,θY=12.25°,Z=42.61 and θZ=291.77°.

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