Answer
$\theta=82.9^{\circ}$
Work Step by Step
$\begin{aligned} \theta & =\cos ^{-1}\left(\frac{\mathbf{r}_{A C^{\cdot}} \mathbf{r}_{A B}}{r_{A C} r_{A B}}\right) \\ & =\cos ^{-1}\left[\frac{(2 \mathbf{i}-8 \mathbf{j}+10 \mathbf{k}) \cdot(-6 \mathbf{i}+2 \mathbf{j}+4 \mathbf{k})}{\sqrt{2^2+(-8)^2+10^2} \sqrt{(-6)^2+2^2+4^2}}\right] \\ & =\cos ^{-1}\left(\frac{12}{96.99}\right) \\ \theta & =82.9^{\circ}\end{aligned}$
