11 Two lines have equations \(\mathbf { r } = \mathbf { i } + 2 \mathbf { j } + \mathbf { k } + \lambda ( a \mathbf { i } + 2 \mathbf { j } - \mathbf { k } )\) and \(\mathbf { r } = 2 \mathbf { i } + \mathbf { j } - \mathbf { k } + \mu ( 2 \mathbf { i } - \mathbf { j } + \mathbf { k } )\), where \(a\) is a constant.
- Given that the two lines intersect, find the value of \(a\) and the position vector of the point of intersection.
- Given instead that the acute angle between the directions of the two lines is \(\cos ^ { - 1 } \left( \frac { 1 } { 6 } \right)\), find the two possible values of \(a\).
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