The points A A\,A and B B\,B have position vectors (4−31)\begin{pmatrix} 4 \\ -3 \\ 1 \end{pmatrix}4−31 and (6−84)\begin{pmatrix} 6 \\ -8 \\ 4 \end{pmatrix}6−84 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 (702)\begin{pmatrix} 7 \\ 0 \\ 2 \end{pmatrix}702 and (55−1)\begin{pmatrix} 5 \\ 5 \\ -1 \end{pmatrix}55−1 respectively. Show that ABPQ ABPQ\,ABPQ is a parallelogram.
309 exam-style questions on Edexcel A Level Maths Vectors, covering 12.1 3D Coordinates, 12.2 Vectors in 3D, 12.3 Solving Geometric Problems, and 12.4 Application to Mechanics. Each one has a worked solution and a mark scheme showing where the marks go.