An art installation is suspended by four anchor points PPP, QQQ, RRR and SSS. Their position vectors relative to an origin OOO are given by
OP→=[−142],OQ→=[350],OR→=[503] and OS→=[1−15] \overrightarrow{OP} = \begin{bmatrix} -1 \\ 4 \\ 2 \end{bmatrix}, \overrightarrow{OQ} = \begin{bmatrix} 3 \\ 5 \\ 0 \end{bmatrix}, \overrightarrow{OR} = \begin{bmatrix} 5 \\ 0 \\ 3 \end{bmatrix} \text{ and } \overrightarrow{OS} = \begin{bmatrix} 1 \\ -1 \\ 5 \end{bmatrix} OP=−142,OQ=350,OR=503 and OS=1−15Find the vector PQ→\overrightarrow{PQ}PQ.
Show that the quadrilateral PQRSPQRSPQRS is a parallelogram, but not a rhombus.
197 exam-style questions on OCR A Level Maths 1.10 Vectors, covering 1.10.1 Vectors in two dimensions, 1.10.2 Vectors in three dimensions (A-level only), 1.10.3 Magnitude and direction of vectors, 1.10.4 Basic operations on vectors, 1.10.5 Position vectors, 1.10.6 Distance between points, 1.10.7 Problem solving using vectors, 1.10.8 Vectors in kinematics, and 1.10 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.