The points A A\,A and B B\,B have position vectors (1−23)\begin{pmatrix} 1 \\ -2 \\ 3 \end{pmatrix}1−23 and (4−25)\begin{pmatrix} 4 \\ -2 \\ 5 \end{pmatrix}4−25 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 (421)\begin{pmatrix} 4 \\ 2 \\ 1 \end{pmatrix}421 and (12−1)\begin{pmatrix} 1 \\ 2 \\ -1 \end{pmatrix}12−1 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.