1 Fig. 6 shows a lean-to greenhouse ABCDHEFG . With respect to coordinate axes \(\mathrm { O } x y z\), the coordinates of the vertices are as shown. All distances are in metres. Ground level is the plane \(z = 0\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{27c27c79-9aea-45a4-a000-41aac70ff866-1_798_1296_354_418}
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\caption{Fig. 6}
\end{figure}
- Verify that the equation of the plane through \(\mathrm { A } , \mathrm { B }\) and E is \(x + 6 y + 12 = 0\).
Hence, given that F lies in this plane, show that \(a = - 2 \frac { 1 } { 3 }\).
- (A) Show that the vector \(\left( \begin{array} { r } 1
- 6
0 \end{array} \right)\) is normal to the plane DHC.
(B) Hence find the cartesian equation of this plane.
(C) Given that G lies in the plane DHC , find \(b\) and the length FG . - Find the angle EFB .
A straight wire joins point H to a point P which is half way between E and \(\mathrm { F } . \mathrm { Q }\) is a point two-thirds of the way along this wire, so that \(\mathrm { HQ } = 2 \mathrm { QP }\).
- Find the height of Q above the ground.