1. The problem statement, all variables and given/known data Consider the two lines, given in the paramentric form L1: x = (0, 1 ,2) + s(1, 0, 2) L2: x = (4, 2, c) + t(-2, 0, d) where c and d are constants. a) For what value of d are the lines parallel? b) With the value of d above, for what value(s) of c (if any) are the two lines identical? Justify briefly. c) For the case c = 5 and d = 0 find the point P on L1 and Q on L2 such that the distance between P and Q is as small as possible. 2. A concept question: Can any vector x with two components be expressed as a linear combination of a and b? Why? 2. Relevant equations ? 3. The attempt at a solution a) I think d = -4, but not sure if that's right. b) I'm not sure how to approach this problem. Do I make 2 + 2s = c - 4t But what do I do after that? c) No clue. I'm thinking perhaps using the dot product = 0? 2. I think a vector can only be expressed as a linear combination of a and b if the two vectors are linearly independent. How do I prove that?