Vector Lines (Edexcel A Level Further Maths: Core Pure): Exam Questions

The line $l_1$ has equation

$\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-4}{3}$

The line $l_2$ has equation

$\mathbf{r}=\mathbf{i}+3\mathbf{k}+t(\mathbf{i}-\mathbf{j}+2\mathbf{k})$

where $t$ is a scalar parameter.

Show that $l_1$ and $l_2$ lie in the same plane.

Find, to the nearest degree, the acute angle between $l_1$ and $l_2$.