How do we check given two vectors, say $a_1\hat{i}+b_1\hat{j}+c_1\hat{k}$ and $a_2\hat{i}+b_2\hat{j}+c_2\hat{k}$ are skew lines ?
I understand that skew lines are those which are neither intersecting nor parallel. i.e, non-coplanar and not intersecting.
So,
I was wondering, can I check it a skew line directly, without checking for whether it is coplanar or intersecting ?