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The volume of a tetrahedron fomed by the...

The volume of a tetrahedron fomed by the coterminus edges `veca , vecb and vecc is 3` . Then the volume of the parallelepiped formed by the coterminus edges `veca +vecb, vecb+vecc and vecc + veca` is

A

6

B

18

C

36

D

9

Text Solution

Verified by Experts

The correct Answer is:
c
`3 =-1/6 [veca vecb vecc] `
`or [veca vecb vecc] =m 18`
volume of the required parallelepiped lt brgt `[ veca + vecb vecb + vecc vecc + veca]`
` 2[veca vecb vecc] =36 `
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If |veca|=2 and |vecb|=3 and veca.vecb=0, " then " (vecaxx(vecaxx(veca...

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  2. If two diagonals of one of its faces are 6hati + 6 hatk and 4 hatj + ...

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  3. The volume of a tetrahedron fomed by the coterminus edges veca , vecb ...

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  4. If veca ,vecb and vecc are three mutually orthogonal unit vectors , th...

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  5. vector vecc are perpendicular to vectors veca= (2,-3,1) and vecb= (1,...

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  6. Given veca=xhati+yhatj+2hatk,vecb=hati-hatj+hatk , vecc=hati+2hatj, ve...

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

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  9. If veca, vecb and vecc are such that [veca vecb vecc] =1, vecc= lambda...

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  10. If 4veca+5vecb+9vecc=0 " then " (vecaxxvecb)xx[(vecbxxvecc)xx(veccxxve...

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  11. Value of [vec a xx vec b,vec a xx vecc,vec d] is always equal to

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  12. Let hata and hatb be mutually perpendicular unit vectors. Then for an...

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  13. Let veca and vecb be unit vectors that are perpendicular to each other...

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  14. veca and vecb are two vectors such that |veca|=1 ,|vecb|=4 and veca. V...

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  15. Then for any arbitary vector veca, (((veca xx vecb) + (veca xx vecb))...

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  16. If veca .vecb =beta and veca xx vecb = vecc ," then " vecb is

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  17. If a(vecalphaxxvecbeta)=b(vecbetaxxvecgamma)+c(vecgammaxxvecalpha)=vec...

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  18. If (vecaxxvecb)xx(vecbxxvecc)=vecb, where veca,vecb and vecc are non z...

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  19. If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and...

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  20. A vector of magnitude 10 along the normal to the curve 3x^2+8x y+2y...

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