(i)[4]
Show that $l$ and $m$ intersect.
(ii)[3]
Calculate the acute angle formed by the lines.
(iii)[5]
Find the equation of the plane containing $l$ and $m$, giving your answer in the form $ax + by + cz = d$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The vector equations of the lines $l$ and $m$ are $\mathbf{r} = \mathbf{i} + \mathbf{j} + \mathbf{k} + s(\mathbf{i} - \mathbf{j} + 2\mathbf{k})$ and $\mathbf{r} = 4\mathbf{i} + 6\mathbf{j} + \mathbf{k} + t(2\mathbf{i} + 2\mathbf{j} + \mathbf{k})$ respectively.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write a general point on $l$ or $m$ in component form, for example $(1+s,1-s,1+2s)$ or $(4+2t,6+2t,1+t)$” …
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