Question

vector direction

Answer 1

Find the unit vector,
\[\frac{\vec{v}}{|\vec{v}|}=\frac{1}{\sqrt{5+z^2}}(1,-2,z)\]
Apply the condition of the problem,
\[\frac{1}{\sqrt{5+z^2}}=\frac{1}{3}\Rightarrow z=\pm 2\]