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 OCR (MEI) A Level Maths 1.11 Vectors, covering 1.11.1 Language of vectors in two dimensions, 1.11.2 Add, subtract and scale vectors, 1.11.3 Magnitude and direction of a vector, 1.11.4 Position vectors, 1.11.5 Distance between points by position vectors, 1.11.6 Vectors to solve problems, 1.11.7 Language of vectors in three dimensions (A-level only), and 1.11 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.