The line L1 has vector equation,  L1 = (  6, 1 ,-1  ) + λ ( 2, 1, 0). The line L2 passes through the points (2, 3, −1) and (4, −1, 1). i) find vector equation of L2 ii)show L2 and L1 are perpendicular.

i)L(r) vector line equations in general are in the form L(r) = p1 + λ (p2) where p1 is any ponit on the line and p2 is the vector direction of the line(unsure how to get the whiteboard up or i would describe this with a diagram)to find the vector diction on the line you work out the vector between two points on the line this is done by subtacting one from the other. (again would show this on a diagram) in this instance for L2, p2 = (2, 3, -1) - (4, -1, 1) = (-2, 4 ,-2) Therefore L2 can either be L2= (2, 3, −1) + λ(-2, 4 ,-2) or L2= (4, −1, 1) + λ(-2, 4 ,-2)ii) for vectors to be perpendicular the vector directions dot products must equal to 0L1 . L2 = 0(2, 1 , 0) . (-2, 4 , -2)= -4 + 4 = 0