(i)[1]
Find a vector equation of the line $AB.$
(ii)[4]
Find the position vector of $P.$
(iii)[4]
Find the equation of the plane that contains $AB$ and is perpendicular to plane $OAB$, and give your answer in the form $ax + by + cz = d.$
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
Relative to the origin $O$, the points $A$ and $B$ have position vectors $ overrightarrow{OA} = i + 2j + 2k$ and $ overrightarrow{OB} = 3i + 4j.$ Point $P$ is on the line $AB$, and $OP$ is at right angles to $AB.$
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Give the correct equation in any equivalent 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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