4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0396f61a-b844-40ed-98d1-82ee2d8a6807-3_643_332_246_870}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a cuboid \(O A B C D E F G\), where \(O\) is the origin, \(A\) has position vector \(5 \mathbf { i } , C\) has position vector \(10 \mathbf { j }\) and \(D\) has position vector \(20 \mathbf { k }\).
- Find the cosine of angle \(C A F\).
Given that the point \(X\) lies on \(A C\) and that \(F X\) is perpendicular to \(A C\),
- find the position vector of point \(X\) and the distance \(F X\).
The line \(l _ { 1 }\) passes through \(O\) and through the midpoint of the face \(A B F E\). The line \(l _ { 2 }\) passes through \(A\) and through the midpoint of the edge \(F G\).
- Show that \(l _ { 1 }\) and \(l _ { 2 }\) intersect and find the coordinates of the point of intersection.