7
\includegraphics[max width=\textwidth, alt={}, center]{1a4ddaa9-1ec2-4138-bfcb-a482fe6c942f-3_394_750_260_699}
The diagram shows a trapezium \(A B C D\) in which \(B A\) is parallel to \(C D\). The position vectors of \(A , B\) and \(C\) relative to an origin \(O\) are given by
$$\overrightarrow { O A } = \left( \begin{array} { l }
3
4
0
\end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { l }
1
3
2
\end{array} \right) \quad \text { and } \quad \overrightarrow { O C } = \left( \begin{array} { l }
4
5
6
\end{array} \right)$$
- Use a scalar product to show that \(A B\) is perpendicular to \(B C\).
- Given that the length of \(C D\) is 12 units, find the position vector of \(D\).