Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Taking O as the origin, the position vectors of points P and Q are \\mathbf{p} and \\mathbf{q} respectively. Point R is arranged so that PQR is a straight line, with Q halfway between P and R.
(a)[3]
Determine the position vector of R in terms of \\mathbf{p} and \\mathbf{q}, and give your answer in simplified form.
(b)[6]
The vector 6\\mathbf{i} + a\\mathbf{j} + b\\mathbf{k} has magnitude 21 and is perpendicular to 3\\mathbf{i} + 2\\mathbf{j} + 2\\mathbf{k}. Determine the possible values of a and b, showing all required working.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply a vector method to obtain \\overrightarrow{OR}=2q-p” …