Line equation in vector product form

A question is this type if and only if it asks to express a line equation in the form (r - a) × d = 0 or to interpret/manipulate this form.

1 questions · Challenging +1.2

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OCR Further Additional Pure AS 2023 June Q4
7 marks Challenging +1.2
4 The equation of line \(l\) can be written in either of the following vector forms.
  • \(\mathbf { r } = \mathbf { a } + \lambda \mathbf { b }\), where \(\lambda \in \mathbb { R }\)
  • \(( \mathbf { r } - \mathbf { c } ) \times \mathbf { d } = \mathbf { 0 }\)
    1. Write down two equations involving the vectors \(\mathbf { a , b , c }\), and d, giving reasons for your answers.
    2. Determine the value of \(\mathbf { a } \cdot ( \mathbf { c } \times \mathbf { d } )\).