The points A A\,A and B B\,B have position vectors (3 −2 1)\begin{pmatrix} 3 \ -2 \ 1 \end{pmatrix}(3 −2 1) and (1 2 −1)\begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}(1 2 −1) respectively.
Find the exact length of ABABAB.
Find the position vector of the midpoint of ABABAB.
The points P P\,P and Q Q\,Q have position vectors (2 1 3)\begin{pmatrix} 2 \ 1 \ 3 \end{pmatrix}(2 1 3) and (4 −3 5)\begin{pmatrix} 4 \ -3 \ 5 \end{pmatrix}(4 −3 5) respectively. Show that ABPQ ABPQ\,ABPQ is a parallelogram.
Practise AQA A Level Maths 1.13 J: Vectors with exam-style questions for A Level Maths. 122 questions covering 1.13.1 Vectors in two and three dimensions, 1.13.2 Magnitude and direction of a vector, 1.13.3 Vector arithmetic, 1.13.4 Position vectors, and 1.13.5 Vectors to solve problems, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
