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If (veca xxvecb) xx (vecc xx vecd) . (ve...

If `(veca xxvecb) 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

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

D

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

Text Solution

Verified by Experts

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-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. [vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to

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  2. The scalars l and m such that lveca + m vecb =vecc, " where " veca, ve...

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  3. If (veca xxvecb) xx (vecc xx vecd) . (veca xx vecd) =0 then which of t...

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

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  5. about to only mathematics

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

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

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  8. If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc= ...

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  9. If vecaxx(vecbxxvecc)=(vecaxxvecb)xxvecc for non coplanar veca,vecb,v...

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  10. A vector vecd is equally inclined to three vectors veca=hati-hatj+hatk...

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  11. A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, ...

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  12. Statement 1: Vector vecc = -5hati + 7 hatj + 2hatk is along the bisec...

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  13. Statement1: A component of vector vecb = 4hati + 2hatj + 3hatk in the ...

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  14. Statement 1: Distance of point D( 1,0,-1) from the plane of points A( ...

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  15. Let vecr be a non - zero vector satisfying vecr.veca = vecr.vecb =vecr...

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  16. Statement 1: If a(1)hati + a(2)hatj + a(3)hatk, b(1)hati+b(2)hatj + b(...

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  17. Statement 1: vecA=2hati + 3hatj + 6hatk , vecB=hati + hatj - 2hatk and...

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  18. Statement 1: veca, vecb and vecc are three mutually perpendicular unit...

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  19. Consider three vectors veca , vecb and vecc Statement 1: vecaxxvecb ...

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  20. Let vecu, vecv and vecw be three unit vectors such that vecu + vecv + ...

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