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If veca, vecb, vecc are any three non co...

If `veca, vecb, vecc` are any three non coplanar vectors, then `[(veca+vecb+vecc, veca-vecc, veca-vecb)]` is equal to

A

`0`

B

`[(veca, vecb, vecc)]`

C

`2[(veca, vecb, vecc)]`

D

`=3[(veca, vecb, vecc)]`

Text Solution

Verified by Experts

The correct Answer is:
D
Clearly,
`[(veca+vecb+vecc, veca-vecc, veca-vecb)]`
`=|(1,1,1),(1,0,-1),(1,-1,0)|=[(veca, vecb, vecc)]=-3[(veca , vecb, vecc)]`
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OBJECTIVE RD SHARMA-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Section I - Solved Mcqs
  1. Let veca, vecb, vecc be three vectors such that [(veca, vecb, vecc)]=2...

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  2. If vecb is a unit vector, then (veca. vecb)vecb+vecbxx(vecaxxvecb) is ...

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  3. If veca, vecb, vecc are any three non coplanar vectors, then [(veca+ve...

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  4. If veca, vecb, vecc are any three non coplanar vectors, then (veca+v...

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  5. Let veca, vecb and vecc be three having magnitude 1,1 and 2 respective...

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  6. If veca=hati+hatj+hatk, veca.vecb=1 and vecaxxvecb=hatj-hatk then vecb

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  7. If veca, vecb, vecc are non-coplanar non-zero vectors, then (vecaxxv...

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  8. If the vectors veca, vecb, vecc and vecd are coplanar vectors, then (...

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  9. (vecaxxvecb).(veccxxvecd) is not equal to

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  10. Let veca=2hati+hatj-2hatk and vecb=hati+hatj. If vecc is a vector such...

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  11. If veca, vecb, vecc are three non colanar, non =null vectors, and vecr...

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  12. The acute angle betwene any two faces of a regular tetrahedron is

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  13. The acute angle that the vector 2hati-2hatj+2hatk makes with the plane...

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  14. If veca, vecb, vecc are non-null non coplanar vectors, then [(veca-2...

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  15. The three vectors hati+hatj, hatj+hatk, hatk+hati taken two at a time ...

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  16. Let G(1),G(2),G(3) be the centroids of the triangular faces OBC, OCA, ...

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  17. Let vecr, veca, vecb and vecc be four non-zero vectors such that vecr....

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  18. Let vecV=2hati+hatj-hatk and vecW=hati+3hatk. It vecU is a unit vector...

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  19. If veca and vecb are two unit vectors, then the vector (veca+vecb)xx(v...

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  20. If vec(alpha)=2hati+3hatj-hatk, vec(beta)=-hati+2hatj-4hatk, vecgamma=...

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