Answer
$||v||=\sqrt {65}$
$θ=119.74°$
Work Step by Step
$v=ai+bj=-4i+7j~~$ ($a\lt0$ and $b\gt0~→~Quadrant~II$)
$||v||=\sqrt {v·v}=\sqrt {(-4i+7j)·(-4i+7j)}=\sqrt {(-4)^2+7^2}=\sqrt {16+49}=\sqrt {65}$
$tan~θ=\frac{b}{a}=\frac{7}{-4}$
$θ=arctan(\frac{7}{-4})+180°=-60.26°+180°=119.74°$
Notice that $-60.26°$ lies in Quadrant IV.
