Mathematics 9709 · AS & A Level · Vectors

Vectors — practice question

Relative to the origin $O$, the position vectors of $A$ and $B$ are $ \overrightarrow{OA} = i + 2j + 2k$ and $\overrightarrow{OB} = 3i + 4j$. Point $P$ is located on the line $AB$, and $OP$ is perpendicular to $AB$.
(i)[1]

Determine a vector equation for the line $AB$.

(ii)[4]

Determine the position vector of $P$.

(iii)[4]

Determine the equation of the plane that contains $AB$ and is perpendicular to the plane $OAB$, and present your answer in the form $ax + by + cz = d$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State the equation of the line correctly in any form, for example $\mathbf{r}=\mathbf{i}+2\mathbf{j}+2\mathbf{k}+\lambda(2\mathbf{i}+2\mathbf{j}-2\mathbf{k})$” …

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