1. The problem statement, all variables and given/known data Is the line through (4,1,-1) and (2,5,3) parallel to the line through (-3,2,0) and (5,1,4)? 2. Relevant equations 3. The attempt at a solution Line one 'direction' = (-2,4,4) = A Line two 'direction' = (8,-1,4) = B I remember that the cross product of two vectors is zero if they are parallel, but AxB is not the zero vector; the answer in the book says they are indeed parallel... Is this not the right method? Cheers, Adrian ^^
If they were parallel, you could write one direction as a scalar multiple of the other. Since you cannot do that as well as the cross-product is not zero, the vectors are not parallel.