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Let vector a ,b and c be three unit vectors such that vector a cross (b cross c)=square root 3/2 (vector b+vector c) vector b is not parallel to vector c

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Solution:    We have  ,

                   veca	imes (vecb	imes vecc)=fracsqrt32(vecb+vecc)

           Rightarrow    (vecacdot vecc)vecb-(vecacdot vecb)vecc=fracsqrt32vecb+fracsqrt32vecc

      We know that  ,

            ecause        left | veca 
ight |=left | vecb 
ight |=left | vecc 
ight |=1

             	herefore         vecacdot vecb=fracsqrt32Rightarrow left | veca 
ight |left | vecb 
ight |cos 	heta=fracsqrt32

            Rightarrow            cos 	heta=fracsqrt32Rightarrow 	heta =frac5pi6.   

Posted by

Deependra Verma

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