4 Points \(A , B\) and \(C\) have position vectors \(\mathbf { a } , \mathbf { b }\) and \(\mathbf { c }\) respectively, relative to origin \(O\). It is given that \(\mathbf { b } \times \mathbf { c } = \mathbf { a }\) and that \(| \mathbf { a } | = 3\).
- Determine each of the following as either a single vector or a scalar quantity.
- \(\mathbf { c } \times \mathbf { b }\)
- \(\mathbf { a } \times ( \mathbf { b } \times \mathbf { c } )\)
- \(\mathbf { a } \cdot ( \mathbf { b } \times \mathbf { c } )\)
- Describe a geometrical relationship between the points \(O , A , B\) and \(C\) which can be deduced from
- the statement \(\mathbf { b } \times \mathbf { c } = \mathbf { a }\),
- the result of (a)(iii).