Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Taking O as the origin, the position vectors of points A and B are given as \(\overrightarrow{OA} = \mathbf{i} - 2\mathbf{j} + 2\mathbf{k}\) and \(\overrightarrow{OB} = 3\mathbf{i} + p\mathbf{j} + q\mathbf{k}\), with p and q as constants.
(i)[2]
State the values of p and q that make \(\overrightarrow{OA}\) parallel to \(\overrightarrow{OB}\).
(ii)[2]
For q = 2p, find the value of p for which angle BOA is \(90^\circ\).
(iii)[3]
For p = 1 and q = 8, find the unit vector in the direction of \(\overrightarrow{AB}\).
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Matches vector components to obtain p=-6” …