(i)[3]
Find the position vector for $A$.
(ii)[4]
Find the acute angle formed by $l$ and $p$.
(iii)[5]
Find an equation of the plane that includes $l$ and is perpendicular to $p$, and give your answer in the form $ax + by + cz = d$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The line $l$ is defined by $\mathbf{r} = 2\mathbf{i} - \mathbf{j} - 4\mathbf{k} + \lambda(\mathbf{i} + 2\mathbf{j} + 2\mathbf{k})$. The plane $p$ has equation $3x - y + 2z = 9$. The point at which $l$ meets the plane $p$ is $A$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write the line’s general point in component form, for example $(2+\lambda,-1+2\lambda,-4+2\lambda)$” …
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