The points A A\,A and B B\,B have position vectors (2−15)\begin{pmatrix} 2 \\ -1 \\ 5 \end{pmatrix}2−15 and (5−53)\begin{pmatrix} 5 \\ -5 \\ 3 \end{pmatrix}5−53 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 (612)\begin{pmatrix} 6 \\ 1 \\ 2 \end{pmatrix}612 and (354)\begin{pmatrix} 3 \\ 5 \\ 4 \end{pmatrix}354 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.