12
9
\end{array} \right) + \lambda \left( \begin{array} { l }
1
3
2
\end{array} \right)$$
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ff20b83a-5e38-437e-8115-5b0a6a54fa9d-2_745_1300_256_399}
\captionsetup{labelformat=empty}
\caption{Fig. 7}
\end{figure}
Fig. 7 illustrates a house. All units are in metres. The coordinates of A, B, C and E are as shown. BD is horizontal and parallel to AE .
- Find the length AE .
- Find a vector equation of the line BD . Given that the length of BD is 15 metres, find the coordinates of D.
- Verify that the equation of the plane ABC is
$$- 3 x + 4 y + 5 z = 30 .$$
Write down a vector normal to this plane.
- Show that the vector \(\left( \begin{array} { l } 4
3
5 \end{array} \right)\) is normal to the plane ABDE . Hence find the equation of the plane ABDE . - Find the angle between the planes ABC and ABDE .