- Relative to a fixed origin \(O\),
the point \(A\) has position vector \(( 2 \mathbf { i } - 3 \mathbf { j } - 2 \mathbf { k } )\)
the point \(B\) has position vector \(( 3 \mathbf { i } + 2 \mathbf { j } + 5 \mathbf { k } )\)
the point \(C\) has position vector ( \(2 \mathbf { i } + 4 \mathbf { j } - 3 \mathbf { k }\) )
The line \(l\) passes through the points \(A\) and \(B\).
- Find the vector \(\overrightarrow { A B }\).
- Find a vector equation for the line \(l\).
- Show that the size of the angle \(C A B\) is \(62.8 ^ { \circ }\), to one decimal place.
- Hence find the area of triangle \(C A B\), giving your answer to 3 significant figures.
The point \(D\) lies on the line \(l\). Given that the area of triangle \(C A D\) is twice the area of triangle \(C A B\),
- find the two possible position vectors of point \(D\).