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A, B and C are three non-zero vectors, no two of them are parallel. If A + B is collinear to C and B + C is collinear to A, then A + B + C is equal to |
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Answer» A `therefore A + B = lambda C` and `B + C = MU A` where, `lambda` and `mu` are SCALARS. `implies A+B+C=(lambda+1)C` and `A+B+C=(mu+1)A` `implies (lambda+1)C=(mu+1)A` If `lambda ne-1`, then `C=(mu+1)/(lambda+1)A` implies C and A are collinear. This is a contradiction to the given CONDITION. `therefore lambda = - 1` `therefore A + B + C = 0` |
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