4 The equation of line \(l\) can be written in either of the following vector forms.
- \(\mathbf { r } = \mathbf { a } + \lambda \mathbf { b }\), where \(\lambda \in \mathbb { R }\)
- \(( \mathbf { r } - \mathbf { c } ) \times \mathbf { d } = \mathbf { 0 }\)
- Write down two equations involving the vectors \(\mathbf { a , b , c }\), and d, giving reasons for your answers.
- Determine the value of \(\mathbf { a } \cdot ( \mathbf { c } \times \mathbf { d } )\).