Chapter 9.5, Problem 36AYU

To determine

To prove: $v=\cos \alpha i+\sin \alpha j$

Answer to Problem 36AYU

Solution:

$v=\cos \alpha i+\sin \alpha j$

Explanation of Solution

Given:

$v$ is a unit vector and the angle between $v$ and $i$ is $\alpha$.

Calculation:

Let $v=ai+bj$,

Since $v$ is a unit vector $\Vert v\Vert =1$,

$\cos \alpha =\frac{a}{\Vert v\Vert }=\frac{a}{1}=a$

$\sin \alpha =\frac{b}{\Vert v\Vert }=\frac{b}{1}=b$

Therefore $v=\cos \alpha i+\sin \alpha j$.