Answer
$||v||=\sqrt {41}$
$θ=51.34°$
Work Step by Step
$v=ai+bj=5i+4j~~$ ($a\gt0$ and $b\gt0~→~Quadrant~I$)
$||v||=\sqrt {v·v}=\sqrt {(5i+4j)·(5i+4j)}=\sqrt {5^2+4^2}=\sqrt {25+16}=\sqrt {41}$
$tan~θ=\frac{b}{a}=\frac{5}{4}$
$θ=arctan(\frac{5}{4})\approx51.34°$
