- Relative to a fixed origin \(O\)
- point \(A\) has position vector \(10 \mathbf { i } - 3 \mathbf { j }\)
- point \(B\) has position vector \(- 8 \mathbf { i } + 9 \mathbf { j }\)
- point \(C\) has position vector \(- 2 \mathbf { i } + p \mathbf { j }\) where \(p\) is a constant
- Find \(\overrightarrow { A B }\)
- Find \(| \overrightarrow { A B } |\) giving your answer as a fully simplified surd.
Given that points \(A , B\) and \(C\) lie on a straight line,
- find the value of \(p\),
- state the ratio of the area of triangle \(A O C\) to the area of triangle \(A O B\).