Distinguish parallel, intersecting and skew lines algebraically

For each pair, test whether the lines are parallel, intersecting or skew. If they intersect, find the position vector of their intersection. All parameters are real.

(a) $l_1:\mathbf r=(1,2,3)+\lambda(1,2,1)$ and $l_2:\mathbf r=(1,3,4)+\mu(2,4,2)$.

(b) $l_1:\mathbf r=(1,2,3)+\lambda(1,2,1)$ and $l_2:\mathbf r=(0,1,5)+\mu(1,3,4)$.

(c) $l_1:\mathbf r=(1,2,3)+\lambda(1,2,1)$ and $l_2:\mathbf r=(0,1,2)+\mu(1,3,4)$.