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If veca, vecb and vecc1 are three non-co...

If `veca, vecb and vecc`1 are three non-coplanar vectors, then `(veca + vecb + vecc). [(veca + vecb) xx (veca + vecc)]` equals

A

0

B

`[veca vecb vecc]`

C

`2[veca vecb vecc]`

D

`-[veca vecb vecc]`

Text Solution

Verified by Experts

The correct Answer is:
d
`(veca+ vecb+vecc).[(veca+vecb)xx(veca+vecc)]`
`= (veca+vecb+vecc).[veca xx veca +vecaxx vecc+vecb xx veca +vecbxxvecc]`
`= (veca +vecb +vecc).[veca xx vecc +vecb xx veca+vecb xxvecc]`
`[veca vecb vecc] -[veca vecb vecc]-[veca vecb vecc]`
`-[veca vecb vecc]`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If veca,vecb and vecc are non coplanar and unit vectors such that veca...

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  2. Let vecu,vecv and vecw be vectors such that vecu+ vecv + vecw =0 if |v...

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  3. If veca, vecb and vecc1 are three non-coplanar vectors, then (veca + v...

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  4. Let vecp,vecq, vecr be three mutually perpendicular vectors of the sam...

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  5. Let veca = 2i + j -2k, and b = i+ j if c is a vector such that veca ....

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  6. Let veca = 2i + j+k, vecb = i+ 2j -k and a unit vector vecc be coplana...

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  7. If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively...

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  8. Let the vectors veca, vecb,vecc and vecd be such that (vecaxxvecb)xx(v...

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  9. If veca, vecb and vecc are unit coplanar vectors , then the scalar tri...

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  10. if hata, hatb and hatc are unit vectors. Then |hata - hatb|^(2) + |hat...

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  11. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

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

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  13. The value of a so thast the volume of parallelpiped formed by vectors ...

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

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  15. The unit vector which is orthogonal to the vector 5hatj + 2hatj + 6hat...

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  16. if veca , vecb and vecc are three non-zero, non- coplanar vectors and ...

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  17. Let veca=hati + 2hatj +hatk, vecb=hati - hatj +hatk and vecc= hati+hat...

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  18. Lelt two non collinear unit vectors hata and hatb form and acute angle...

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  19. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb).(ve...

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  20. Two adjacent sides of a parallelogram A B C D are given by vec A B...

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