Classify four pairs of spatial lines and find acute angles

Find whether the following pairs of lines are parallel, intersecting or skew. If they intersect, find the point of intersection and the acute angle between the lines.

(a) $\mathbf r=(1,-1,1)+\lambda(3,4,1)$, $\lambda\in\mathbb R$, and $\mathbf r=(1,2,3)+\mu(9,12,3)$, $\mu\in\mathbb R$.

(b) $\mathbf r=(1,0,3)+s(2,1,1)$, $s\in\mathbb R$, and $\mathbf r=(2,-1,1)+t(1,-2,0)$, $t\in\mathbb R$.

(c) $\mathbf r=4\mathbf i+8\mathbf j+3\mathbf k+\alpha(\mathbf i+2\mathbf j+\mathbf k)$, $\alpha\in\mathbb R$, and $\mathbf r=7\mathbf i+6\mathbf j+5\mathbf k+\beta(6\mathbf i+4\mathbf j+5\mathbf k)$, $\beta\in\mathbb R$.

(d) $\mathbf r=(4,2,1)+\lambda(2,1,-2)$, $\lambda\in\mathbb R$, and the z-axis.

[Hint: The z-axis has equation $\mathbf r=\gamma(0,0,1)$, $\gamma\in\mathbb R$.]