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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

Answers (1)

D Deependra Verma

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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