(a)[3]
When $\vec{OA}$ is perpendicular to $\vec{OB}$, find the value of $p$.
(b)[4]
When $OAB$ is a straight line, find $\vec{OA}$ and $\vec{OB}$. Also determine the length of the line $OA$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
With respect to an origin $O$, the position vectors of points $A$ and $B$ are $\vec{OA} = \begin{pmatrix} p - 6 \\ 2p - 6 \\ 1 \end{pmatrix}$ and $\vec{OB} = \begin{pmatrix} 4 - 2p \\ p \\ 2 \end{pmatrix}$, where $p$ is a constant.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set the scalar product to zero and make an attempt at the solution” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI