Points $A$ and $B$ are defined by the position vectors $\overrightarrow{OA} = \mathbf{i} - 2\mathbf{j} + 2\mathbf{k}$ and $\overrightarrow{OB} = 3\mathbf{i} + \mathbf{j} + \mathbf{k}$. The line $l$ is described by $\mathbf{r} = 2\mathbf{i} + \mathbf{j} + m\mathbf{k} + \mu(\mathbf{i} - 2\mathbf{j} - 4\mathbf{k})$, where $m$ is a constant.
(i)[5]
Find the value of $m$, given that line $l$ intersects the line through $A$ and $B$.
(ii)[5]
Find the equation of the plane parallel to $\mathbf{i} - 2\mathbf{j} - 4\mathbf{k}$ and passing through $A$ and $B$. Give your answer in the form $ax + by + cz = d$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use a correct method to obtain a vector equation for $AB$” …