- Relative to a fixed origin \(O\).
- the point \(A\) has position vector \(2 \mathbf { i } - 3 \mathbf { j } + 5 \mathbf { k }\)
- the point \(B\) has position vector \(8 \mathbf { i } + 3 \mathbf { j } - 7 \mathbf { k }\)
The line \(l\) passes through \(A\) and \(B\).
- Find \(\overrightarrow { A B }\)
- Find a vector equation for the line \(l\)
The point \(C\) has position vector \(3 \mathbf { i } + 5 \mathbf { j } + 2 \mathbf { k }\)
The point \(P\) lies on \(l\)
Given that \(\overrightarrow { C P }\) is perpendicular to \(l\)
- find the position vector of the point \(P\)