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=5−36
Write down the vector AB→\overrightarrow{AB}AB.
Show that ABCDABCDABCD is a parallelogram, but not a rhombus.
