Home
Class 12
MATHS
Let veca, vecb, vecc be three non-zero n...

Let `veca, vecb, vecc` be three non-zero non coplanar vectors and `vecp, vecq` and `vecr` be three vectors given by `vecp=veca+vecb-2vecc, vecq=3veca-2vecb+vecc` and `vecr=veca-4vcb+2vecc`
If the volume of the parallelopiped determined by `veca, vecb` and `vecc` is `V_(1)` and that of the parallelopiped determined by `veca, vecq` and `vecr` is `V_(2)`, then `V_(2):V_(1)=`

A

2

B

`1/3`

C

`1/2`

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    MARVEL PUBLICATION|Exercise PREVIOUS YEARS MHT-CET EXAM QUESTIONS|10 Videos

  • VECTORS

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|20 Videos

  • TRIGONOMETRIC FUNCTIONS

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP: CHAPTER 3-3.3|13 Videos

Similar Questions

Explore conceptually related problems

Let veca, vecb, vecc be three non - zero, non - coplanar vectors and vecp, vecq, vecr be three vectors given by vecp=veca+2vecb-2vecc, vecq=3veca+vecb -3vecc and vecr=veca-4vecb+4vecc . If the volume of parallelepiped determined by veca, vecb and vecc is v_(1) cubic units and volume of tetrahedron determined by vecp, vecq and vecr is v_(2) cubic units, then (v_(1))/(v_(2)) is equal to

If veca, vecb, vecc , be three on zero non coplanar vectors estabish a linear relation between the vectors: 7vec+6vecc, veca+vecb+vec, 2veca-vecb+vecc, vec-vecb-vecc

If veca, vecb, vecc , be three on zero non coplanar vectors estabish a linear relation between the vectors: veca+3vecb=3vecc, veca-2vecb+3vecc, vec+5vecb-2vecc,6veca=14vecb+4vecc

If veca, vecb, vecc are non coplanar vectors and vecp, vecq, vecr are reciprocal vectors, then (lveca+mvecb+nvecc).(lvecp+mvecq+nvecr) is equal to

veca , vecb and vecc are three non-coplanar vectors and vecr . Is any arbitrary vector. Prove that [vecbvecc vecr]veca+[vecc veca vecr]vecb+[vecavecbvecr]vecc=[veca vecb vecc]vecr .

If veca, vecb, vecc are three non-coplanar vectors, then a vector vecr satisfying vecr.veca=vecr.vecb=vecr.vecc=1 , is

If veca, vecb, vecc are three non-zero non-null vectors are vecr is any vector in space then [(vecb, vecc, vecr)]veca+[(vecc, veca, vecr)]vecb+[(veca, vecb, vecr)]vecc is equal to

If veca, vecb, vecc are any three non coplanar vectors, then (veca+vecb+vecc).(vecb+vecc)xx(vecc+veca)

If veca, vecb and vecc are three non - zero and non - coplanar vectors such that [(veca,vecb,vecc)]=4 , then the value of (veca+3vecb-vecc).((veca-vecb)xx(veca-2vecb-3vecc)) equal to

If veca, vecb, vecc are any three non coplanar vectors, then [(veca+vecb+vecc, veca-vecc, veca-vecb)] is equal to

MARVEL PUBLICATION-VECTORS-TEST YOUR GRASP
  1. Let veca, vecb, vecc be three non-zero non coplanar vectors and vecp, ...

    Text Solution

    |

  2. If ABCDEF is a regular hexagon , then bar(AB) + bar(AC) + bar(AE) + ...

    Text Solution

    |

  3. If the origin is the centroid of a triangle ABC having vertices A(a ,1...

    Text Solution

    |

  4. If alpha,beta ,gamma are direction angles of a line , then cos 2alpha ...

    Text Solution

    |

  5. If |bar(u)| = sqrt(3) and bar(u) is equally inclined to co - ordinate...

    Text Solution

    |

  6. If vectors 2i-j+k,i+2j-3k and 3i+aj+5k are coplaner, then a=

    Text Solution

    |

  7. If bara.i = 4, then bara.[j xx (2j - 3k)]=

    Text Solution

    |

  8. The vector bar(AB)=3hati+4hatk and bar(AC)=5hati-2hatj+4hatk are the s...

    Text Solution

    |

  9. If veca vecb are non zero and non collinear vectors, then [(veca, vecb...

    Text Solution

    |

  10. If bara,barb,barc are non-coplaner vectors and barp=(barbxxbarc)/([bar...

    Text Solution

    |

  11. If direction ratios of two lines are 2,-6,-3 and 4,3,-1 then directi...

    Text Solution

    |

  12. If the volumes of parallelepiped with coterminus edges -pj+5k,i-j+qk a...

    Text Solution

    |

  13. A line makes 45^(@) with OX, and equal angles with OY and OZ. Then the...

    Text Solution

    |

  14. If the points with position vectors -i + 3j + 2k , -4i + 2j - 2k and 5...

    Text Solution

    |

  15. If bara.barb=barb.barc=barc.bara=0 and bara,barb,barc form a right-han...

    Text Solution

    |

  16. If bara,barb,barc are non-coplaner vectors, then (bara.(barbxxbarc))/...

    Text Solution

    |

  17. i · (j xx k) + j · (k xx i) + k · (i xx j ) =

    Text Solution

    |

  18. If bara=2i+3j-k,barb=-i+2j-4k and barc=i+j+k, then (baraxxbarb).(barax...

    Text Solution

    |

  19. If vectors 2hati-hatj+hatk ,hati+2hatj-3hatk and 3hati+mhatj+5hatk are...

    Text Solution

    |

  20. 2i · (j xx k) - 3j · (i xx k) - 4k · (i xx j) =

    Text Solution

    |

  21. If vectors bara,barb,barc are non-coplaner, then ([bara+2barb barb+2...

    Text Solution

    |