4.
Relative to a fixed origin \(O\),
- the point \(A\) has position vector \(5 \mathbf { i } + 3 \mathbf { j } - 2 \mathbf { k }\)
- the point \(B\) has position vector \(7 \mathbf { i } + \mathbf { j } + 2 \mathbf { k }\)
- the point \(C\) has position vector \(4 \mathbf { i } + 8 \mathbf { j } - 3 \mathbf { k }\)
- Find \(| \overrightarrow { A B } |\) giving your answer as a simplified surd.
Given that \(A B C D\) is a parallelogram,
find the position vector of the point \(D\).
The point \(E\) is positioned such that
- \(A C E\) is a straight line
- \(A C : C E = 2 : 1\)
- Find the coordinates of the point \(E\).