What is the difference between parallel same and parallel different vectors? And if we are given two vector equations of lines that are skew, how can we know that the lines are skew?

Question

faiqraees · Answer

@hartnn

hartnn · Answer

I am not sure about those definitions, but from the names, i think:
parallel same are co-incident vectors.
parallel different are parallel vectors with non-0 distance between them...

skew lines are non-coplanar and non-parallel .
so you need to actually check these conditions from vector equations.

faiqraees · Answer

No i mean what a technique I should employ to work out whether two lines are skew.

faiqraees · Answer

like if two lines are intersecting, we equate the x y and z coordinates and if there occurs a single solution, then its intersecting and if the coordinates cancels each other out then they are parallel

faiqraees · Answer

But what conditions should I check for to know whether the lines are skew?

hartnn · Answer

so, check whether they are intersecting or not, with what you mentioned,
if intersecting, check whether they are coplanar or not, with any of the ways you know.
If non-coplanar too, then the lines are skew.