Answer
b) $\|\vec{v}\|=3$
a) $k=\pm 5 / 3$
Work Step by Step
It's given that $\|\vec{v}\|=3$
a) If $5=\|k \vec{v}\|,$ then
\[
\|k \vec{v}\|=|k|\|\vec{v}\|=|k|(3)=5 \Rightarrow k=\pm \frac{5}{3}
\]
b) If $k=-2$ , $\|k \vec{v}\|=6$: :
\[
\begin{aligned}
6=\|k \vec{v}\| & \Rightarrow|k|\|\vec{v}\|=6 \\
& \Rightarrow\|\vec{v}\|=6 /|k|=\frac{6}{|-2|}=3
\end{aligned}
\]
