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BITSAT2012MathematicsVector AlgebraActual

If a .b =a .c and a b=a c , then correct statement is

Options

  1. Aa |( b - c )
  2. Ba (b-c)
  3. Ca=0 or b=c
  4. DNone of these

Correct answer

C. a=0 or b=c

Step-by-step solution

a . b .=a c a (b-c)=0 a =0 or b - c =0 or a ( b - c ) a =0 or b = c or a ( b - c ) Also a x b=a x c a (b-c)=0 a =0 or b - c =0 or a |( b - c ) a=0 or b=c or a |(b-c) Observing to ( 1 ) and ( 2 ) we find that a =0 or b = c

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