## Precalculus (10th Edition)

$v=4\sqrt2i+4\sqrt2j.$
If a vector $v=ai+bj$ makes an angle of $\alpha$ with the positive x-axis and has magnitude $||v||=\sqrt{a^2+b^2}$, then $a=||v||cos\alpha$ and $v=||v||sin\alpha$. Hence here $a=||8||cos(45^\circ)=4\sqrt2$ and $v=||8|sin(45^\circ)=4\sqrt2$. Therefore $v=4\sqrt2i+4\sqrt2j.$