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If veca, vecb and vecc are non -coplanar...

If `veca, vecb and vecc` are non -coplanar unit vectors such that `vecaxx(vecbxxvecc)=(vecb+vecc)/sqrt2,vecb and vecc` are non- parallel , then prove that the angle between `veca and vecb` is ` 3pi//4`

Text Solution

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`vecaxx(vecbxxvecc)=(vecbxxvecc)/sqrt2`
`(veca .vecc)vecb-(veca.vecb)vecc=1/sqrt2vecb+1/sqrt2vecc`
Since `vecb and vecc` are non-collinear, comparing coefficients of `vecc` on both sides of (i) , we get
`-veca.vecb=1/sqrt2or veca.vecb=-1/sqrt2`
`(1) (1) cos theta=-1/sqrt2`
Where `theta` is the angle between `veca and vecb` .therefore,
`cos theta=-1/sqrt2or cos theta=cos135^(@)or theta=135^(@)=3pi//4`
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