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[vecaxx vecb " " vecc xx vecd " " vecex...

`[vecaxx vecb " " vecc xx vecd " " vecexx vecf]` is equal to

A

`[veca vecb vecd] [vecc vece vecf]-[veca vecb vecc] [vecd vece vecf]`

B

`[veca vecb vece ] [vecf vecc vecd] - [veca vecb vecf] [vece vecc vecd] `

C

`[vecc vecd veca] [vecb vece vecf] - [veca vecd vecb] [vecavece vecf]`

D

`[veca vecc vece] [vecb vecd vecf]`

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Verified by Experts

The correct Answer is:
a,b,c
Let `vecA=vecaxxvecb, vecB=veccxxvecd and vecC=vecexxvecf`
we know that
`vecA.(vecB xx vecC)=vecB. (vecCxx vecA) = vecC.(vecAxx vec B) `
`(vecaxx vecb).[(veccxxvecd) xx (vecexxvecf)]`
`(vecaxxvecb) .[{(veccxx vecd).vecf} vece. {(vecc xx vecd) vece} vecf}`
`[vecc vecd vecf] [vecavecb vece] - [vecc vecd vece] [veca vecb vecf]`
similarly, other parts can be obtained .
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If veca, vecb and vecc are three unit vectors such that veca xx (vecb ...

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

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  3. [vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to

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

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

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

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  7. about to only mathematics

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

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

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

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

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

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

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

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

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

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

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

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

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

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