Answer Happy

1 Choose the correct answer (3' x 6) (1) Two nonzero vectors ã and are parallel if and only if (>. (A) 2-6= 0; (B) x6 = 0; (C) axb=1; (D) a.5=-1. (2) The geometric series maq", 4 #0 is convergent if and only if(). (A) 451; (B) 4 <1; (C) <1: (D) lol 21. (3) Suppose that the diagonals AC = ã and BD = 7 of the parallelogram ABCD are given. Then AB = (A) a +b; (B) a = 5; (c) }(+5); (D) }ä – ). (1) Suppose that i = 1 + 23 - 2Ē. Then ||(). (A) 1: (B) 2; (C)3; (D) 4. (5) Suppose that i = (1,1,1) and 5 = (2,3,4). Then ä-6=( ). (A) (0,1,2): (B) (1,2,3); (C) (2.3.4); (D) (3,4,5). (6) Suppose that a = (0,1,0), 5 = (2, -2, 1) and the included angle is . Then a 6=( ). (A) 1: (B) $ (C)2: (D) 2 True or False (3 x 5) Please judge the following statements. Write T (True) or F (False) only. (1) ( ) Harmonie series is convergent. (2) () If two nonzero vectors ū and 6 are perpendicular, then a x6 =0. (3) Suppose that $(xv) in partial derivable at (x0, xo), then f(x,y) miast be continuous at (x0, ). 3x - 4y= 1. ()+(3.2) (5) ) The set 1 - {€R!|-1 -1} is an open set.