   Chapter 11.1, Problem 55E

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 ‖ = 2 ,       θ u = 4 ‖ v ‖ = 1 ,       θ v = 2

To determine

To calculate: The x-component and y-component of u+v where magnitude of v is v=1 and makes an angle θv=2 with positive x-axis and magnitude of u is u=2 and makes an angle θu=4 with positive x-axis.

Explanation

Given:

Magnitude of v is v=1 and makes an angle θv=2 with positive x-axis and magnitude of u is u=2 and makes an angle θu=4 with positive x-axis.

Formula used:

If the magnitude of vector v is v and it makes an angle θ with the positive x–axis then v=vcosθi+vsinθj

Calculation:

Since, the angle between v and positive x-axis is 2.

Hence,

v=vcosθvi+vsinθvj=1cos2i+1sin2j=1(0.999)i+1(0.035)j

That is,

=(0

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