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.

(a) Given that the two lines intersect, find the value of \(a\) and the position vector of the point of intersection.

(b) 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 \(a\).