The points $A$ and $B$ are given by the position vectors $\mathbf{i} + 2\mathbf{j} - \mathbf{k}$ and $3\mathbf{i} + \mathbf{j} + \mathbf{k}$, respectively. The line $l$ is defined by $\mathbf{r} = 2\mathbf{i} + \mathbf{j} + \mathbf{k} + \mu(\mathbf{i} + \mathbf{j} + 2\mathbf{k})$.
(i)[5]
Show that $l$ does not intersect the line through $A$ and $B$.
(ii)[5]
The plane $m$ is at right angles to $AB$ and passes through the midpoint of $AB$. It meets the line $l$ at the point $P$. Determine the equation of $m$ and the position vector of $P$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the correct method to obtain the vector equation of $AB$.” …