2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{045545c7-06d9-40b6-9d01-fc792ab0aa07-01_222_241_525_2042}
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\caption{Figure 1}
\end{figure}
The points \(A , B\) and \(C\) have position vectors \(\mathbf { a } , \mathbf { b }\) and \(\mathbf { c }\) respectively, relative to a fixed origin \(O\), as shown in Figure 1.
It is given that
$$\mathbf { a } = \mathbf { i } + \mathbf { j } , \quad \mathbf { b } = \mathbf { 3 i } - \mathbf { j } + \mathbf { k } \quad \text { and } \quad \mathbf { c } = \mathbf { 2 i } + \mathbf { j } - \mathbf { k } .$$
Calculate
- \(\mathbf { b } \times \mathbf { c }\),
- \(\mathbf { a . } ( \mathbf { b } \times \mathbf { c } )\),
- the area of triangle \(O B C\),
- the volume of the tetrahedron \(O A B C\).