- Relative to a fixed origin \(O\)
- the point \(A\) has position vector \(4 \mathbf { i } - 3 \mathbf { j } + 5 \mathbf { k }\)
- the point \(B\) has position vector \(4 \mathbf { j } + 6 \mathbf { k }\)
- the point \(C\) has position vector \(- 16 \mathbf { i } + p \mathbf { j } + 10 \mathbf { k }\)
where \(p\) is a constant.
Given that \(A , B\) and \(C\) lie on a straight line,
- find the value of \(p\).
The line segment \(O B\) is extended to a point \(D\) so that \(\overrightarrow { C D }\) is parallel to \(\overrightarrow { O A }\) (b) Find \(| \overrightarrow { O D } |\), writing your answer as a fully simplified surd.