   Chapter 11.1, Problem 56E

Chapter
Section
Textbook Problem

# Finding a Vector In Exercises 53-56, find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis. ‖ u ‖ = 5 ,       θ u = − 0.5 ‖ v ‖ = 5 ,       θ v = − 0.5

To determine

To calculate: The component form of u+v, if u=5, v=5, θu=0.5, and θv=0.5.

Explanation

Given:

The lengths of u and v are: u=5 and v=5.

And the angles are: θu=0.5 and θv=0.5.

Formula used:

If the angle between u and positive x-axis is θ.

Then,

u=ucosθi+usinθj

Calculation:

Since, u=5 and θu=0.5.

Then,

u=5cos(0.5)i+5sin(0.5)j=5cos(0.5)i5sin(0

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