Home
Class 11
MATHS
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 `
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Reasoning type|8 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Comprehension type|27 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE ENGLISH|Exercise All Questions|691 Videos

Similar Questions

Explore conceptually related problems

Volume of parallelpiped formed by vectors veca xx vecb, vecb xx vecc and vecc xx veca is 36 sq. units.

If V is the volume of the parallelepiped having three coterminous edges as veca,vecb and vecc , then the volume of the parallelepiped having three coterminous edges as vecalpha = (veca.veca)veca+(veca.vecb)vecb+(veca.vecc)vecc , vecbeta=(vecb.veca)veca+(vecb.vecb)+(vecb.vecc)vecc and veclambda=(vecc.veca)veca+(vecc.vecb)vecb+(vecc.vecc)vecc is

Volume of the parallelopiped whose adjacent edges are vectors veca , vecb , vecc is

If the volume of the parallelepiped formed by the vectors veca xx vecb, vecb xx vecc and vecc xx veca is 36 cubic units, then the volume (in cubic units) of the tetrahedron formed by the vectors veca+vecb, vecb+vecc and vecc + veca is equal to

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

The volume of a tetrahedron determined by the vectors veca, vecb, vecc is (3)/(4) cubic units. The volume (in cubic units) of a tetrahedron determined by the vectors 3(veca xx vecb), 4(vecbxxc) and 5(vecc xx veca) will be

If [(veca,vecb,vecc)]=3 , then the volume (in cubic units) of the parallelopiped with 2veca+vecb,2vecb+vecc and 2vecc+veca as coterminous edges is

If the volume of the parallelopiped formed by the vectors veca, vecb, vecc as three coterminous edges is 27 units, then the volume of the parallelopiped having vec(alpha)=veca+2vecb-vecc, vec(beta)=veca-vecb and vec(gamma)=veca-vecb-vecc as three coterminous edges, is

If |veca|=5, |vecb|=3, |vecc|=4 and veca is perpendicular to vecb and vecc such that angle between vecb and vecc is (5pi)/6 , then the volume of the parallelopiped having veca, vecb and vecc as three coterminous edges is

Prove that [ veca+ vecb , vecb+ vecc , vecc+ veca]=2[ veca , vecb , vecc] .

CENGAGE ENGLISH-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. If |veca|=2 and |vecb|=3 and veca.vecb=0, " then " (vecaxx(vecaxx(veca...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(2)hatj+b(3)hatk and vecc=c(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. value of [vecaxxvecbvecaxxvecc vecd] is always equal to

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. If vecb and vecc are unit vectors, then for any arbitary vector veca,...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. if (vecaxxvecb)xx(vecbxxvecc)=vecb, " where " veca, vecb and vecc are ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |