The points A A\,A and B B\,B have position vectors (2 1 −3)\begin{pmatrix} 2 \ 1 \ -3 \end{pmatrix}(2 1 −3) and (5 −1 0)\begin{pmatrix} 5 \ -1 \ 0 \end{pmatrix}(5 −1 0) 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 (4 2 1)\begin{pmatrix} 4 \ 2 \ 1 \end{pmatrix}(4 2 1) and (1 4 −2)\begin{pmatrix} 1 \ 4 \ -2 \end{pmatrix}(1 4 −2) respectively. Show that ABPQ ABPQ\,ABPQ is a parallelogram.
Practise Edexcel A Level Maths Vectors with exam-style questions for A Level Maths. 100 questions covering 12.1 3D Coordinates, 12.2 Vectors in 3D, 12.3 Solving Geometric Problems, and 12.4 Application to Mechanics, matched to the Edexcel A Level Maths (9MA0) 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.