Let u, v and w be the vectors in R given by u = 5[0, -2, 5] + 4[-1, -1, 1], v= 5[0, -2, 5] - 3[-1, -1, 1], and w = -7u + 5v. Write w as a linear combination of [0, -2, 5] and [-1, -1, 1]. W= [0, -2, 5] + [-1,-1, 1]= Enter a vector in RS as [x, y, z]. Check For v and we R if lly - wll =4, llvl/ = 6 and ||wll = 9 Then v . W = (Hint: Use the fact that ||v - wl|2 = (v - w) . (v - w).) If e is the angle between the vectors v and w, then cos 0 = Let proj w be the projection of w to v. Then (proj,w) . v = Check (a) (1 mark) If u, v E RS are such that Ilu - 2vll = |lu + 2vil, then we must have U . V= (b) (3 marks) For any such vectors, we must also have 113u + 6v112 + 116u - 3v/12 = allu|12 + 6liv/12+ c(u. v) when a = ,b = , and c =