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Let G(1),G(2),G(3) be the centroids of t...

Let `G_(1),G_(2),G_(3)` be the centroids of the triangular faces OBC, OCA, OAB of a tetrahedron OABC. If `V_(1)` denotes the volume of the tetrahedron OABC and `V_(2)` denotes the volume of the paralellopiped with `OG_(1),OG_(2)OG_(3)` as three concurrent edges then

A

`4V_(1)=9V_(2)`

B

`9V_(1)=4V_(2)`

C

`3V_(1)=2V_(2)`

D

`3V_(2)=2V_(1)`

Text Solution

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A
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AAKASH SERIES-APPENDICES (REVISION EXERCISE)-MULTIPLE PRODUCT OF TWO VECTORS
  1. If veca, vecb, vecc are three coplanar vectors, barp, barq, barr are n...

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  2. If bara=3bari+2barj+bark,barb=bari+barj+2bark and barc=bari+3barj+3bar...

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  3. Let G(1),G(2),G(3) be the centroids of the triangular faces OBC, OCA, ...

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  4. bara,barb,barc are non coplanar and bard=x(bara xx barb) +y(barb xx ba...

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  5. barb and barc are non collinear vectors. bara is a vector such that b...

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  6. Let bara=bari+2hatj+3hatk, barb= -bari+2hatj+3bark, barc=3hati+hatj an...

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  7. If bara, barb, barc are three vectors of magnitudes sqrt(3), 1, 2 such...

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  8. The angle between the line barr=(2bari-barj+bark)+lambda(bari-barj+bar...

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  9. If barb, barc are two unit vectors along the positive x, y axes, and b...

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  10. If x(bara xx barb) +y(barb xx barc)+z(barc xx bara)=barr and [(bara, b...

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  11. If A=(1, -2, -1), B= (4, 0, -3), C = (1, 2, -1), D=(2, -4, -5), then d...

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  12. A tetrahedron of volume V = 5 has three of its vertices at the points ...

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  13. If bara, barb, barc are three vectors such that |barb|=|barc| then {(...

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  14. Angle between the line barr = (-bari+3barj+3bark)+t(2bari+3barj+6bark)...

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  15. If 4x + i(3x-y) =3+ i(-6), where x and y are real numbers, then find t...

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  16. If bara=(1)/(sqrt(10)) (3bari+bark) and barb=(1)/(7)(2bari+3barj-6bar...

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  17. The vectors veca and barb are not perpendicular and barc and bard are ...

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  18. If vecx=3hati-6hatj-hatk, vecy=hati+4hatj-3hatk and vecz=3hati-4hatj-1...

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  19. Let veca = 2 hati+hatj-2hatk, vecb=hati+hatj. If vecc is a vector suc...

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  20. The shortest distance between the z-axis and the line x+y+2z-3=0=2x+3y...

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