Problem

With respect to a fixed origin $O$ the points $A$ and $B$ have position vectors

$$\begin{pmatrix}6\\6\\2\end{pmatrix} \text{ and } \begin{pmatrix}6\\0\\7\end{pmatrix}$$

respectively.

The line $l_1$ passes through the points $A$ and $B$.

(a) Write down an equation for $l_1$

Give your answer in the form $\mathbf{r}=\mathbf{p}+\lambda \mathbf{q}$, where $\lambda$ is a scalar parameter.

The line $l_2$ has equation

$$\mathbf{r}=\begin{pmatrix}3\\1\\4\end{pmatrix}+\mu \begin{pmatrix}1\\5\\9\end{pmatrix}$$

where $\mu$ is a scalar parameter.

(b) Show that $l_1$ and $l_2$ do not meet.

The point $C$ is on $l_2$ where $\mu=-1$

(c) Find the acute angle between $AC$ and $l_2$

Give your answer in degrees to one decimal place.