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Manipal MET2015MathematicsVector Algebra

Let a,b and c be non-zero vectors such that no two are collinear and (a b) c= 1 3 |b||c| a . If is the acute angle between the vectors b and c , then equals

Options

  1. A2 2 3
  2. B2 3
  3. C2 3
  4. D1 3

Correct answer

A. 2 2 3

Step-by-step solution

We have, (a b) c= 1 3 |b||c| a aligned & (a c) b-(b c) a= 1 3 |b||c| a & (a c) b- (b c)+ 1 3 |b||c| a=0 & a c=0 and b c+ 1 3 |b||c|=0 & [ a, b are non-collinear ] aligned aligned & | b || c | + 1 3 | b || c |=0 & =- 1 3 & = 1- ^2 = 1- (- 1 3 )^2 aligned = 1- 1 9 = 8 9 = 2 2 3

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