13 The points A and B have coordinates \(( 4,0 , - 1 )\) and \(( 10,4 , - 3 )\) respectively. The planes \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\) have equations \(x - 2 y = 5\) and \(2 x + 3 y - z = - 4\) respectively.
- Find the acute angle between the line AB and the plane \(\Pi _ { 1 }\).
- Show that the line AB meets \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\) at the same point, whose coordinates should be specified.
- Find \(( \mathbf { i } - 2 \mathbf { j } ) \times ( 2 \mathbf { i } + 3 \mathbf { j } - \mathbf { k } )\).
- Hence find the acute angle between the planes \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\).
- Find the shortest distance between the point A and the line of intersection of the planes \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\).