1. The problem statement, all variables and given/known data Let l1:x=3+t, y=1-t, z=2t and l2:x=-1+s, y=2s, z=1+kt (not sure if this one is just a typo, in which t should actually be s, or whether this is fundamental to the problem) be two lines in R3. a) Find all value(s) of k, (if any) for which l1 and l2 are parallel. If not possible then explain why. a) Find all value(s) of k, (if any) for which l1 and l2 are perpendicular. If not possible then explain why. 2. Relevant equations These two lines are given in parametric forms, from which I should be able to get the directional vector, and the point associated with each one. 3. The attempt at a solution After noticing that I could grab a little information about each line, I decided to take a look at their directional vectors. [tex]l_1: <1,-1,2>[/tex] [tex]l_2: <1,2,k>[/tex] I'm assuming I'm supposed to be solving for k in this problem? after looking at these, I can't see them being proportional to each other, so I don't think they are parallel, granted, I'm not sure how to necessarily show this mathematically. My biggest problem is finding all k in which these may be perpendicular, the only idea I've been playing around with would be that if I took the Dot Product between the directional vectors of line 1 and line 2, it would need to equal 0 in order for these two lines to be perpendicular, but I'm not sure if this is the right track of thinking, since I'm not sure what to do about k. Is my thinking somewhere along the right lines, or have I made a horrible mistake? Any help would be great.