The points A A\,A and B B\,B have position vectors (−132)\begin{pmatrix} -1 \\ 3 \\ 2 \end{pmatrix}−132 and (3−21)\begin{pmatrix} 3 \\ -2 \\ 1 \end{pmatrix}3−21 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 (540)\begin{pmatrix} 5 \\ 4 \\ 0 \end{pmatrix}540 and (191)\begin{pmatrix} 1 \\ 9 \\ 1 \end{pmatrix}191 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.