## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$i$
Let us consider two vectors $v=pi+qj$ and $w=xi+yj$; then we have the unit vector $u$ in the same direction as $v$ given by: $u=\dfrac{v}{||v||}$ and the magnitude of any vector (let us say $v$) can be determined using the formula $||v||=\sqrt{p^2+q^2}$ We have: $||v||=\sqrt {5^2+0}=5$ Therefore, $u=\dfrac{v}{||v||}=\dfrac{5 i}{5}=i$