(a)[3]
Show that $AB = 2CD$.
(b)[3]
Find the angle between the directions of $\overrightarrow{AB}$ and $\overrightarrow{CD}$.
(c)[4]
Show that the line through $A$ and $B$ does not meet the line through $C$ and $D$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
Taking origin $O$ as the reference point, the position vectors of the points $A$, $B$, $C$ and $D$ are $\vec{OA} = \begin{pmatrix} 2 \\ 1 \\ 5 \end{pmatrix}$, $\vec{OB} = \begin{pmatrix} 4 \\ -1 \\ 1 \end{pmatrix}$, $\vec{OC} = \begin{pmatrix} 1 \\ 1 \\ 2 \end{pmatrix}$ and $\vec{OD} = \begin{pmatrix} 3 \\ 2 \\ 3 \end{pmatrix}$.