(a)[2]
Determine a unit vector in the direction of $l$.
(b)[2]
The line $m$ goes through the points $A$ and $B$. Find a vector equation for $m$.
(c)[5]
Decide whether lines $l$ and $m$ are parallel, intersecting or skew.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The line $l$ is described by $\mathbf{r} = \mathbf{i} - 2\mathbf{j} - 3\mathbf{k} + \lambda(-\mathbf{i} + \mathbf{j} + 2\mathbf{k})$. The points $A$ and $B$ are given by the position vectors $-2\mathbf{i} + 2\mathbf{j} - \mathbf{k}$ and $3\mathbf{i} - \mathbf{j} + \mathbf{k}$ respectively.