10 The equations of two straight lines are $$\mathbf { r } = \mathbf { i } + \mathbf { j } + 2 a \mathbf { k } + \lambda ( 3 \mathbf { i } + 4 \mathbf { j } + a \mathbf { k } ) \quad \text { and } \quad \mathbf { r } = - 3 \mathbf { i } - \mathbf { j } + 4 \mathbf { k } + \mu ( - \mathbf { i } + 2 \mathbf { j } + 2 \mathbf { k } ) ,$$ where \(a\) is a constant.

1. Given that the acute angle between the directions of these lines is \(\frac { 1 } { 4 } \pi\), find the possible values of \(a\).
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2. Given instead that the lines intersect, find the value of \(a\) and the position vector of the point of intersection.