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  • If vectors a , b and c are non -coplanar unit vectors such that a cross (b cross c) = vec b+ vec c / square root 2 then the angle between vec a and vec b

If vectors a , b and c are non -coplanar unit vectors such that a cross (b cross c) = vec b+ vec c / square root 2 then the angle between vec a and vec b

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Solution:   Since   

                    veca imes (vecb imes vecc)=fracvecb+veccsqrt2

Therefore ,      (vecacdot vecc)vecb-(vecacdot vecb)vecc=frac1sqrt2vecb+frac1sqrt2vecc

Since    vecb   and   vecc  are non coplanar

 \ \ Rightarrow hspace1cmvecacdot vecc=frac1sqrt2hspace0.5cmand hspace0.5cmvecacdot vecb=frac1sqrt2\ \ Rightarrow hspace0.5cmcos heta =-frac1sqrt2Rightarrow heta=frac3pi4

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Deependra Verma

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