Question P2.8: In each case, set up the dot product to find the angle θ. Do......

a. \mathbf{r}_{A}=\{3 \mathbf{k}\} \mathrm{m}, \quad r_{A}=3 \mathrm{~m}

\mathbf{r}_{B}=\{2 \mathbf{i}+2 \mathbf{j}-1 \mathbf{k}\} \mathrm{m}, \quad r_{B}=3 \mathrm{~m}

\mathbf{r}_{A} \cdot \mathbf{r}_{B}=0(2)+0(2)+(3)(-1)=-3 \mathrm{~m}^{2}

\mathbf{r}_{A} \cdot \mathbf{r}_{B}=r_{A} r_{B} \cos \theta

-3=3(3) \cos \theta

b. \mathbf{r}_{A}=\{-2 \mathbf{i}+2 \mathbf{j}+1 \mathbf{k}\} \mathrm{m}, \quad r_{A}=3 \mathrm{~m}

\mathbf{r}_{B}=\{1.5 \mathbf{i}-2 \mathbf{k}\} \mathrm{m}, \quad r_{B}=2.5 \mathrm{~m}

\mathbf{r}_{A} \cdot \mathbf{r}_{B}=(-2)(1.5)+2(0)+(1)(-2)=-5 \mathrm{~m}^{2}

\mathbf{r}_{A} \cdot \mathbf{r}_{B}=r_{A} r_{B} \cos \theta

-5=3(2.5) \cos \theta