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Let veca, vecb, vecc be three unit vecto...

Let `veca, vecb, vecc` be three unit vectors such that `veca. vecb=veca.vecc=0`, If the angle between `vecb` and `vecc` is `(pi)/3` then the volume of the parallelopiped whose three coterminous edges are `veca, vecb, vecc` is

A

`(sqrt(3))/2` cubic units

B

`1/2` cubit unit

C

1 cubic unit

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`veca.vecb=veca.vecc=0impliesveca_|_vecb, veca_|_veccimpliesveca||vecbxxvecc`
Also `|vecbxxvecc|=|vecb||vecc|"sin"(pi)/3=(sqrt(3))/2 [ :' |vecb|=|vecc|=1]`
`:.|[(veca, vecb, vecc)]|=|veca, vecbxxvecc|=|veca||vecbxxvecc|=(sqrt(3))/2`
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OBJECTIVE RD SHARMA-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Section I - Solved Mcqs
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  2. Let veca=2hati+3hatj-hatk and vecb=hati-2hatj+3hatk. Then , the value ...

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  3. Let veca, vecb, vecc be three unit vectors such that veca. vecb=veca.v...

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  4. If veca, vecb, vecc are three non coplanar, non zero vectors then (vec...

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  5. If the acute angle that the vector alphahati+betahatj+gammahatk makes ...

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  6. If veca, vecb, vecc are non coplanar vectors and vecp, vecq, vecr are ...

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  7. If veca vecb are non zero and non collinear vectors, then [(veca, vecb...

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  8. If vecr is a unit vector such that vecr=x(vecbxxvecc)+y(veccxxveca)+...

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  9. Let veca, vecb, vecc be three vectors such that [(veca, vecb, vecc)]=2...

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

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

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

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

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

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

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

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

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

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

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

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