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If (veca xx vecb) xx (vecc xx vecd) . (v...

If `(veca xx vecb) xx (vecc xx vecd) . (veca xx vecd) =0` then which of the following may be true ?

A

`veca, vecb and vecd` are nenessarily coplanar

B

`veca` lies iin the plane of `vecc and vecd`

C

`vecvb` lies in the plane of `veca and vecd`

D

`vecc` lies in the plane of `veca and vecd`

Text Solution

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The correct Answer is:
b,c,d
`(vecaxxvecb )xx(vecc xx vecd). (vecaxxvecd) =0`
`or ([veca vecc vecd] vecb- [vecb vecc vecd]veca) . (veca xx vecd)=0`
`or [veca veccvecd] [vecb veca vecd] =0`
Hence, either `vecc or vecb` must lie in the plane of ` veca and vecd`.
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CENGAGE ENGLISH-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  6. if veca xx vecb = vecc ,vecb xx vecc = veca , " where " vecc ne vec0 ...

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  7. Let veca, vecb, and vecc be three non- coplanar vectors and vecd be a ...

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  8. If veca, vecb and vecc are three unit vectors such that veca xx (vecb ...

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  9. If in triangle ABC, vec(AB) = vecu/|vecu|-vecv/|vecv| and vec(AC) = (...

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  13. A,B C and dD are four points such that vec (AB) = m(2 hati - 6 hatj +...

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  14. If the vectors veca, vecb, vecc are non -coplanar and l,m,n are distin...

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  15. Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(...

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  16. If vectors vecA=2hati+3hatj+4hatk, vecB=hati+hatj+5hatk and vecC form ...

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