PART 1: 1. (9 marks) Find lu + ull, lu - ull, du in the following cases (a) u = NO v = 1 = 3 (b) u = /3 U = -1.5 72 10 1 = e3 (c) 12 u = * = 25 2. (6 marks) Using a sketch, explain why the inequality 1/2+ 2ll = 1/zell+ 1/211 must hold for any vectors u, v. Under what conditions on u and v are the left- and right-hand side equal? 3. (5 marks) You are given that for any two vectors a, b E R" the "dot product" is defined as a . b = a1b1 + a2b2 + .. . + anbn, where ai, bi are the i'th elements of a, b. Show that