The points A A\,A and B B\,B have position vectors (−253)\begin{pmatrix} -2 \\ 5 \\ 3 \end{pmatrix}−253 and (21−1)\begin{pmatrix} 2 \\ 1 \\ -1 \end{pmatrix}21−1 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 (7−5−2)\begin{pmatrix} 7 \\ -5 \\ -2 \end{pmatrix}7−5−2 and (3−12)\begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}3−12 respectively. Show that ABPQ ABPQ\,ABPQ is a parallelogram.
67 exam-style questions on Edexcel A Level Maths 12.3 Solving Geometric Problems. Each one has a worked solution and a mark scheme showing where the marks go.