I REALLY NEED HELP WITH MY VECTORS ASSIGNMENT

1. Given a and b, with la + b| = V3, determine (2a - 56) . (b + 3a). 2. a). Determine a unit vector that is perpendicular to both 4i + j + 3k and i - 2j + 5k. b). Given v = [3, -1, -2], determine the integer components of u such that v x u = [4,2,5] and |ul = 3. 3. Given a, b, c are vectors in 3, such that (c x b) . a = -4, determine a . [(b + c) x (c + a)]. 4. Suppose a, b, c are distinct, non-zero vectors. Prove that a x b = a x c when a is collinear with b - C