Answer
$b) \vec{v}=\pm \hat{\jmath}$
$c) \vec{v}=\pm \hat{\imath}$
$a) \vec{v}=\pm \hat{k}$
Work Step by Step
a) If a vector $\vec{v}$ is perpendicular to the $x y$ -plane, then it's parallel to the $z$ -axis. If its initial point is at the origin $O(0,0,0)$ the terminal point is (0,0,-1) or (0,0,1) . So:
\[
\vec{v}=\pm\langle 0,0,1\rangle=\pm \hat{k}
\]
b) Analogously: In this case, $\vec{v}$ is parallel to the $y$ -axis. The unit vectors in the direction of this axis are $\pm \hat{\jmath}$. So:
\[
\pm \hat{\jmath}=\vec{v}
\]
c)
In the latter case, $\ {v} $ is parallel to the $ x $ axis, so:
\[
\pm \hat{\imath}=\vec{v}
\]
