A quadrilateral has vertices AAA, BBB, CCC and DDD with position vectors given by
OA→=[2−14],OB→=[523],OC→=[805] and OD→=[5−36] \overrightarrow{OA} = \begin{bmatrix} 2 \\ -1 \\ 4 \end{bmatrix}, \overrightarrow{OB} = \begin{bmatrix} 5 \\ 2 \\ 3 \end{bmatrix}, \overrightarrow{OC} = \begin{bmatrix} 8 \\ 0 \\ 5 \end{bmatrix} \text{ and } \overrightarrow{OD} = \begin{bmatrix} 5 \\ -3 \\ 6 \end{bmatrix} OA=2−14,OB=523,OC=805 and OD=5−36Write down the vector AB→\overrightarrow{AB}AB.
Show that ABCDABCDABCD 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.