Hi all working through Anton and Busby.., if i have two vectors, v = (1,2,1)s and v = (9,6,0) + (0,1,-1)t how can i show that they do not intersect in 3-space ?
By trying to find a point where they intersect! If these two lines intersected at (x, y, z), then we would have (x, y, z)= (s, 2s, s)= (9, 6+ t, -t) so we have s= 9, 2s= 6+ t, s= -t. Since the first equation tells you what s is, the third equation tells you what t must be. Do those values satisfy the second equation.