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If vec a , vec b and vec c are non-copl...

If ` vec a , vec b and vec c` are non-coplanar unit vectors such that ` vec axx( vec bxx vec c)=( vec b+ vec c)/(sqrt(2))` , then the angle between ` vec a and vec b` is a. `3pi//4` b. `pi//4` c. `pi//2` d. `pi`

Text Solution

Verified by Experts

`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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