Vectors \(\mathbf i\) and \(\mathbf j\) are unit vectors parallel to the \(x\)-axis and \(y\)-axis respectively.

(a) The vector \(\mathbf v\) has magnitude \(3\sqrt5\) and has the same direction as \(\mathbf i-2\mathbf j\). Find \(\mathbf v\) in the form \(a\mathbf i+b\mathbf j\), where \(a\) and \(b\) are integers.

(b) The velocity vector \(\mathbf w\) makes an angle of \(30^\circ\) with the positive \(x\)-axis and \(|\mathbf w|=2\). Find \(\mathbf w\) in the form \(\sqrt c\,\mathbf i+d\mathbf j\), where \(c\) and \(d\) are integers.