- Vectors \(\mathbf { u }\) and \(\mathbf { v }\) are given by
$$\mathbf { u } = 5 \mathbf { i } + 4 \mathbf { j } - 3 \mathbf { k } \quad \text { and } \quad \mathbf { v } = a \mathbf { i } - 6 \mathbf { j } + 2 \mathbf { k }$$
where \(a\) is a constant.
- Determine, in terms of \(a\), the vector product \(\mathbf { u } \times \mathbf { v }\)
Given that
- \(\overrightarrow { A B } = 2 \mathbf { u }\)
- \(\overrightarrow { A C } = \mathbf { v }\)
- the area of triangle \(A B C\) is 15
- determine the possible values of \(a\).