- Relative to a fixed origin \(O\), the point \(A\) has position vector \(( 10 \mathbf { i } + 2 \mathbf { j } + 3 \mathbf { k } )\), and the point \(B\) has position vector \(( 8 \mathbf { i } + 3 \mathbf { j } + 4 \mathbf { k } )\).
The line \(l\) passes through the points \(A\) and \(B\).
- Find the vector \(\overrightarrow { A B }\).
- Find a vector equation for the line \(l\).
The point \(C\) has position vector \(( 3 \mathbf { i } + 12 \mathbf { j } + 3 \mathbf { k } )\).
The point \(P\) lies on \(l\). Given that the vector \(\overrightarrow { C P }\) is perpendicular to \(l\), - find the position vector of the point \(P\).