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.
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.