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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

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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 the two diagonals of one its faces are 6 hat i+6 hat ka n d4 hat ...

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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 vec c is perpendicular to vectors vec a=(2,-3,1)a n d vec b...

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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(2)hatj+b(3)hatk and vecc=c(...

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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 4 vec a+5 vec b+9 vec c=0, then ( vec axx vec b)xx[( vec bxx vec c)...

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  11. Value of [ vec axx vec b vec axx vec c vec d] is always equal to ( vec...

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  12. Let vec aa n d vec b be mutually perpendicular unit vectors. Then f...

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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( vecalphaxx vecbeta)+b( vecbetaxx vecgamma)+c( vecgammaxx vecalph...

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  18. If veca xx vecb = vecb xx vecc ne 0 where veca , vecb and vecc are co...

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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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