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AP EAMCET201726 Apr 2017Morning ShiftMathematicsVector AlgebraActual

If a , b and c are non-zero vectors such that a and b are not perpendicular to each other, then the vector r which is perpendicular to a and satisfying r b = c b is

Options

  1. A( a b ) c c a
  2. Bb ( a c ) b c
  3. C( b c ) a a b
  4. D( c b ) a a c

Correct answer

C. ( b c ) a a b

Step-by-step solution

Given that, a, b and c are non-zero vectors such that a & b are not perpendicular. Also given, r b = c b a ( r b )= a ( c b ) Since, r a , therefore a . r =0 aligned & ( a b ) r -( a r ) b = a ( c b ) & ( a b ) r = a ( c b ) aligned aligned & = a ( c b ) a b =- [( c b ) a ] a b & =- [-( b c ) a ] a b = ( b c ) a a b aligned

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