'C 43. Prove Theorem 2. I. 44. Prove Theorem 2.2. 45. Prove Thcorcrn 2.5 46. Show that the sum of two vera is wei! defined (se definition of the sum). ' 47. Show that ai + bj s ci + djifand only ita e (and.2l Directed Line Segments and Vectors 5'7 13 V x ' Is '+21 l4v=-3i-j V : .. ' ' 4' + 31 16. v = 43 In P -' roblems 17-24, find the endpomts of the representative AB of v from the given information. /. 17 v = 3i - j,A : (1,4) Vl's'f'v = 2i + 3j,A = (-l.3) by /l9v= -i+2j,B=(4,2) 20.v=2i-4j,3=(03) 21. v : i - j,A = (5,1) 22. v = 2i + LA = (-2.0) 23v=3i-j,3=(42) 24v=2i+2j,B=(11) In Problems 25-32,find u + v and u - v. Draw a diagram showing u, V, II + V. and 'l - V 25fiu=3i-j,v=i+2j v26."ii=2i+3j,v=2i-j vziu=i'-j,v=2i+2j 28u=3i+j, =2i 2.9u=i-3j,v=2i+4j 30u=4i+j,v=i+2j 3Lu=3i-j,v=2i-2j A 32u=i-j,v=2i+j ' Given the vectors of Figure 2.11, sketch u + v. 34. Given the vectors of Figure 2.11, sketch u -- v. (b) (3