With reference to the origin $O$, the position vectors of $A$ and $B$ are $2\mathbf{i} + 4\mathbf{k}$ and $5\mathbf{i} + \mathbf{j} + 6\mathbf{k}$ respectively. The line $l_1$ passes through $A$ and $B$.
(a)[2]
Determine a vector equation for the line $l_1$.
(b)[4]
The line $l_2$ has equation $\mathbf{r} = 2\mathbf{i} + \mathbf{j} + 5\mathbf{k} + \mu(\mathbf{i} + 2\mathbf{j} + 3\mathbf{k})$. Show that $l_1$ and $l_2$ do not intersect.
(c)[3]
Determine the acute angle between the directions of $l_1$ and $l_2$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the correct method to form the equation of $l_1$” …