With respect to a fixed origin OOO, the points AAA and BBB have position vectors
(231) and (4−14) \begin{pmatrix} 2 \\ 3 \\ 1 \end{pmatrix} \text{ and } \begin{pmatrix} 4 \\ -1 \\ 4 \end{pmatrix} 231 and 4−14respectively. The line l1l_1l1 passes through the points AAA and BBB.
Write down an equation for l1l_1l1 in the form r=p+λq\mathbf{r} = \mathbf{p} + \lambda \mathbf{q}r=p+λq.
The line l2l_2l2 has equation
r=(12−3)+μ(1−12) \mathbf{r} = \begin{pmatrix} 1 \\ 2 \\ -3 \end{pmatrix} + \mu \begin{pmatrix} 1 \\ -1 \\ 2 \end{pmatrix} r=12−3+μ1−12Show that l1l_1l1 and l2l_2l2 do not meet.
The point CCC is on l2l_2l2 where μ=2\mu = 2μ=2.
Find the acute angle between the line segment ACACAC and the line l2l_2l2. Give your answer in degrees to one decimal place.
