question_answer 41)

                  The vectors A, B and C add up to zero. Find which is false.                 (a) \[A\times B\times C\] is not zero unless B, C are parallel. (b) \[(A\times B).C\] is not zero unless B, C are parallel. (c) If A, B, C define a plane, \[(A\times B)\times C\] is in that plane                 (d) \[(A\times \,B)\,.\,C=\,|A|\,|B|\,+|C|\,\to \,{{C}^{2}}\,={{A}^{2}}+{{B}^{2}}\]

Answer:

                  (c)