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.
42 exam-style questions on OCR (MEI) A Level Maths 1.11.7 Language of vectors in three dimensions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.