2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8b3dd4a1-b270-4bd7-88d6-fe10601f9d74-03_333_360_328_794}
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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
$$\mathbf { a } = \mathbf { i } + \mathbf { j } , \quad \mathbf { b } = 3 \mathbf { i } - \mathbf { j } + \mathbf { k } \quad \text { and } \quad \mathbf { c } = 2 \mathbf { i } + \mathbf { j } - \mathbf { k } .$$
Calculate
- \(\mathbf { b } \times \mathbf { c }\),
- a.(b \(\times \mathbf { c ) }\),
- the area of triangle \(O B C\),
- the volume of the tetrahedron \(O A B C\).