Answer
$$\theta=123^{\circ}$$
Work Step by Step
$\text{The magnitude of $\vec{r}$ is }$ $|\vec{r}|=\sqrt{(9.0 \mathrm{m})^{2}+(6.0 \mathrm{m})^{2}+(-7.0 \mathrm{m})^{2}}=12.9 \mathrm{m} .$ $\text{The angle between $\vec{r}$ and the $z$ -axis is given by}$ $$\cos \theta=\frac{\vec{r} \cdot \hat{\mathrm{k}}}{|\vec{r}|}=\frac{-7.0 \mathrm{m}}{12.9 \mathrm{m}}=-0.543$$ which implies $\theta= \cos^{-1} (-0.543) =123^{\circ}$
