6. The points \(A\) and \(B\) have position vectors \(2 \mathbf { i } + 6 \mathbf { j } - \mathbf { k }\) and \(3 \mathbf { i } + 4 \mathbf { j } + \mathbf { k }\) respectively.
The line \(l _ { 1 }\) passes through the points \(A\) and \(B\).
- Find the vector \(\overrightarrow { A B }\).
- Find a vector equation for the line \(l _ { 1 }\).
A second line \(l _ { 2 }\) passes through the origin and is parallel to the vector \(\mathbf { i } + \mathbf { k }\). The line \(l _ { 1 }\) meets the line \(l _ { 2 }\) at the point \(C\).
- Find the acute angle between \(l _ { 1 }\) and \(l _ { 2 }\).
- Find the position vector of the point \(C\).