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Given two lines in space, either they are parallel, or they intersect or they are skew. Determine whether the lines taken two at a time, are parallel, intersect or are skew. If they intersect find the point of intersection.

line 1: x=1+2t, y=-1-t, z=3t; -infiniti<t<infiniti

line 2: x=2-s, y=3s, z=1+2; -infiniti<s<infiniti

line 3: x=5+2r, y=1-r, z=8+3r; -infiniti<r<infiniti

I'm not really sure where to go with this. I found the normal vector forms of the equations and I don't think any of them are parallel using the cross product=0 when vectors are parallel but i have no idea how to find itnersection or skew when given the parametric equations. Did I do the parallel part right? and where would I begin for the other parts. Do you use each part (x,y,z) from the parametric as three points to find the equation of the plane formed?

Thanks so much for any help