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The volume of the tetrahedron whose vert...

The volume of the tetrahedron whose vertices are the points `hati, hati+hatj, hati+hatj+hatk` and `2hati+3hatj+lamdahatk` is `1//6` units,
Then the values of `lamda`

A

does not exist

B

is 7

C

is -1

D

is any real value

Text Solution

Verified by Experts

The correct Answer is:
D
Let ABCD be the given tetradehron. Then
`vec(AB)=hatj,vec(AC)=hatj+hatk` and `vec(AD)=hati+3hatj+lamdahatk`
`:.` volume `=1/6`
`implies1/6[(vec(AB), vec(AC),vec(AD))]=1/6`
`implies[(vec(AB),vec(AC),vec(AD))]=1`
`=(vec(AB)xxvec(AC).vec(AD))=1`
`implieshati.(hati+K3hatj+lamda hatk)=1`, which is true for all values of `lamda`
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OBJECTIVE RD SHARMA-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Exercise
  1. The volume of the tetrahedron whose vertices are the points hati, hati...

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  2. For non zero vectors veca,vecb, vecc |(vecaxxvecb).vec|=|veca||vecb|...

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  3. Let veca=hati+hatj-hatk, vecb=hati-hatj+hatk and vecc be a unit vector...

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  4. If veca lies in the plane of vectors vecb and vecc, then which of the ...

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  5. The value of [(veca-vecb, vecb-vecc, vecc-veca)], where |veca|=1, |vec...

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  6. If veca, vecb, vecc are three non-coplanar mutually perpendicular unit...

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  7. If vecr.veca=vecr.vecb=vecr.vecc=0 for some non-zero vectro vecr, then...

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  8. If the vectors vecr(1)=ahati+hatj+hatk, vecr(2)=hati+bhatj+hatk, vecr(...

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  9. If hata, hatb, hatc are three units vectors such that hatb and hatc ar...

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  10. For any three vectors veca, vecb, vecc the vector (vecbxxvecc)xxveca e...

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  11. For any these vectors veca,vecb, vecc the expression (veca-vecb).{(vec...

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  12. For any vectors vecr the value of hatixx(vecrxxhati)+hatjxx(vecrxxha...

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  13. If the vectors veca=hati+ahatj+a^(2)hatk, vecb=hati+bhatj+b^(2)hatk, v...

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  14. Let veca, vecb, vecc be three non-coplanar vectors and vecp,vecq,vecr ...

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  15. If veca, vecb, vecc are non-coplanar vectors, then (veca.(vecbxxvecc))...

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  16. Let veca=a(1)hati+a(2)hatj+a(3)hatk, vecb=b(1)hati+b(2)hatj+b(3)hatk a...

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  17. If the non zero vectors veca and vecb are perpendicular to each other,...

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  18. Prove that: [(vecaxxvecb)xx(vecaxxvecc)].vecd=pveca vecb vecc](veca.ve...

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  19. If (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) then

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  20. If veca,vecb,vecc and vecp,vecq,vecr are reciprocal system of vectors,...

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  21. vecaxx(vecaxx(vecaxxvecb)) equals

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