7 The line \(L _ { 1 }\) passes through the point \(( 3,6,1 )\) and is parallel to the vector \(2 \mathbf { i } + 3 \mathbf { j } - \mathbf { k }\). The line \(L _ { 2 }\) passes through the point ( \(3 , - 1,4\) ) and is parallel to the vector \(\mathbf { i } - 2 \mathbf { j } + \mathbf { k }\).

1. Write down vector equations for the lines \(L _ { 1 }\) and \(L _ { 2 }\).
2. Prove that \(L _ { 1 }\) and \(L _ { 2 }\) intersect, and find the coordinates of their point of intersection.
3. Calculate the acute angle between the lines.