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Let vec a, vec b, and vec c be three non...

Let `vec a, vec b, and vec c` be three non coplanar unit vectors such that the angle between every pair of them is `pi/3`. If `vec a xx vec b+ vecb xx vec x=p vec a + q vec b + r vec c` where p,q,r are scalars then the value of `(p^2+2q^2+r^2)/(q^2)` is

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`vec(a), vec(b), vec(c) `are three unit vectors with angle`pi/3` between them.
`[ veca vecb vecc ]^2=|(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc)|`
`|(1,1/2,1/2),(1/2,1,1/2),(1/2,1/2,1)|=1/2`
thus`[ veca vecb vecc ]=1/sqrt2`
Given `veca xx vecb +vecb xx vecc=pveca+qvecb+rvecc`...(1)
take dot product of(1) with `veca`
=>`1/sqrt2=p+q/2+r/2`.....(2)
take dot product of(1) with `vecb`
...
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