Measured from origin $O$, the position vectors of $A$, $B$ and $C$ are given by $\vec{OA} = \begin{pmatrix}2\\1\\3\end{pmatrix}$, $\vec{OB} = \begin{pmatrix}4\\3\\2\end{pmatrix}$ and $\vec{OC} = \begin{pmatrix}3\\-2\\-4\end{pmatrix}$. The quadrilateral $ABCD$ is a parallelogram.
(a)[3]
Find the position vector for $D$.
(b)[3]
The angle between $BA$ and $BC$ is $\theta$. Determine the exact value of $\cos\theta$.
(c)[4]
Hence determine the area of $ABCD$, with your answer in the form $p\sqrt{q}$, where $p$ and $q$ are integers.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain a valid vector for one side of the parallelogram, for example $\vec{AB}=(2,2,-1)$.” …