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1)

Let a,b and c be three non-zero vectors such that no two of them are collinear and  (a xb)xc =   13|b||c|a.   . If θ is the angle between vectors b and c, then a value of   sinθ  is


A) 223

B) 23

C) 23

D) 233

Answer:

Option A

Explanation:

 Given,

   (a x b)x c=  13|b||c|a.

               -c x (a x b) = 13|b||c|a.

           (c.b).a+(c.a)b=13|b||c|a

             [13|b||c|+(c.b)]a=(c.a)b

  Since a  and b are not collinear

          c.b+13|b||c|=0   and c.a=0

         |c||b|cosθ+13|b||c|=0

      |b||c|(cosθ+13)=0

     cosθ+13=0,(|b|0,|c|0)

      cosθ=13

      sinθ=83=223