Answer
$79.8^{\circ}$
Work Step by Step
$\vec{r}_{1}\cdot\vec{r}_{2}=(2.70\times-4.10)+(-2.90\times3.30)+(5.50\times5.40)= 9.06\,m^{2}$
$|\vec{r}_{1}|=\sqrt {(2.70)^{2}+(-2.90)^{2}+(5.50)^{2}}=6.78\,m$
$|\vec{r}_{2}|=\sqrt {(-4.10)^{2}+(3.30)^{2}+(5.40)^{2}}=7.54\,m$
$\theta=\cos^{-1}(\frac{\vec{r}_{1}\cdot\vec{r}_{2}}{|\vec{r}_{1}||\vec{r}_{2}|})=\cos^{-1}(\frac{9.06}{6.78\times7.54})=79.8^{\circ}$
