8 11 points previous answers scalcet7 124053 suppose

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8. 1/1 points | Previous Answers SCalcET7 12.4.053. Suppose that a 0 (a) If a · b = a · c , does it follow that b . = c ?
(b) If a × b = a × c , does it follow that b = c ?
(c) If a · b = a · c , and a × b = a × c , does it follow that b = c ? Solution or Explanation (a) No. If a · b = a · c , then a · ( b c ) = 0, so a is perpendicular to b c , which can happen if b c . For example, let and
(b) No. If a × b = a × c , then a × ( b c ) = 0 , which implies that a is parallel to b c , which of course can happen if b c . (c) Yes. Since a · c = a · b , a is perpendicular to b c , by part (a). From part (b), a parallel to b c . Thus since a 0 but is both parallel and perpendicular to b c , we have b c = 0 , so b = is also c .

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