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

If `veca, vecb, vecc` are non-coplanar unit vectors such that `vecaxx(vecbxxvecc)=(vecb+vecc)/(sqrt(2))` then the angle between `veca` and `vecb` is

A

`pi/4`

B

`pi/2`

C

`(3pi)/(4)`

D

`pi`

Text Solution

Verified by Experts

The correct Answer is:
C
`veca xx (vecb xx vecc) =(overset(-)(b)+overset(-)(c))/(sqrt2) rArr overset(-)(a).overset(-)(c))overset(-)(b)-(overset(-)(a) overset(-)(b))overset(-)(c)=(overset(-)(b)+overset(-)(c))/(sqrt2)`
`rArr [(overset(-)(a).overset(-)(c)-1/sqrt2]overset(-)(b)-[(overset(-)(a).overset(-)(b))+1/sqrt2]overset(-)(c)=0`
`rArr |veca||vecc| cos theta=1/sqrt2, |veca||vecb| cos phi=-1/sqrt2`
`rArr cos theta=1/sqrt2, cos phi=-1/sqrt2 rArr theta=pi/4, phi=(3pi)/(4)`
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