The points A A\,A and B B\,B have position vectors (1−24)\begin{pmatrix} 1 \\ -2 \\ 4 \end{pmatrix}1−24 and (3−52)\begin{pmatrix} 3 \\ -5 \\ 2 \end{pmatrix}3−52 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 (253)\begin{pmatrix} 2 \\ 5 \\ 3 \end{pmatrix}253 respectively. Show that ABPQ ABPQ\,ABPQ is a parallelogram.
168 exam-style questions on AQA A Level Maths 1.13 J: Vectors, covering 1.13.1 Vectors in two and three dimensions, 1.13.2 Magnitude and direction of a vector, 1.13.3 Vector arithmetic, 1.13.4 Position vectors, and 1.13.5 Vectors to solve problems. Each one has a worked solution and a mark scheme showing where the marks go.