Home
Class 12
MATHS
If the volume of the parallelopiped with...

If the volume of the parallelopiped with a, b and c as coterminous edges is 40 cubic units, then the volume of the parallelopiped having `b+c, c+a and a+b` as coterminous edges in cubic units is

A

80

B

120

C

160

D

40

Text Solution

Verified by Experts

The correct Answer is:
A
Given , volume of parallelopied `[abc]=40`
`therefore` Volume of parallelopiped `=[b+c c+a a +b]=2[abc]`
`2xx40=80` cu units. .
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise (VECTORS ) Exercise 2 ( Topical problems )|88 Videos

  • VECTORS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise ( MHT CET Corner)|66 Videos

  • TRIGONOMETRIC FUNCTIONS OF COMPOUND ANGLES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 2 (MISCELLANEOUS PROBLEMS)|20 Videos

Similar Questions

Explore conceptually related problems

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

The volume of a parallelopiped whose coterminous edges are 2veca , 2vecb , 2 vec c , is

Statement 1: Let V_(1) be the volume of a parallelopiped ABCDEF having veca, vecb, vecc as three coterminous edges and V_(2) be the volume of the parallelopiped PQRSTU having three coterminous edges as vectors whose magnitudes are equal to the areas of three adjacent faces of the parallelopiped ABCDEF . Then V_(2)=2V_(1)^(2) Statement 2: For any three vectors vec(alpha), vec(beta), vec(gamma) [vec(alpha)xxvec(beta),vec(beta)xxvec(gamma),vec(gamma)xxvec(alpha)]=[(vec(alpha),vec(beta),vec(gamma))]^(2)

The volume of the parallelopiped, if a=3hati,b=5hatj and c=4hatk are coterminous edges of the parallelopiped is

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-VECTORS -( MHT CET Corner)
  1. If the volume of the parallelopiped with a, b and c as coterminous edg...

    Text Solution

    |

  2. If a=hat(i)+hat(j)-2hat(k), b=2hat(i)-hat(j)+hat(k) and c=3hat(i)-hat(...

    Text Solution

    |

  3. If M and N are the mid-points of the diagonals AC and BD respectively ...

    Text Solution

    |

  4. If G(barg), H(barh) and P(barp) are centroid, orthocenter and circumce...

    Text Solution

    |

  5. If a=hat(i)+hat(j)+hat(k), b=2hat(i)+lambda hat(j)+hat(k), c=hat(i)-ha...

    Text Solution

    |

  6. If the position vectors of the vertices A, B and C are 6i, 6j ...

    Text Solution

    |

  7. If three vectors 2hat(i)-hat(j)-hat(k), hat(i)+2hat(j)-3hat(k) and 3ha...

    Text Solution

    |

  8. Find a vector of magnitude 9, which is perpendicular to both vectors 4...

    Text Solution

    |

  9. If in a Delta ABC, O and O' are the incentre and orthocentre respectiv...

    Text Solution

    |

  10. If a+b+c=0 and |a|=5, |b|=3 and |c|=7, then angle between a and b is

    Text Solution

    |

  11. If vecu=veca-vecb,vecv=veca+vecb and |veca|=|vecb|=2, then |vecuxxvecv...

    Text Solution

    |

  12. If a, b, c are linearly independent vectors and delta =|(a,b,c),(a.a,a...

    Text Solution

    |

  13. If veca,vecb,vecc are three non- coplanar vectors and vecp,vecq,vecr a...

    Text Solution

    |

  14. The volume of a parallelopiped whose coterminous edges are 2veca , 2ve...

    Text Solution

    |

  15. The position vectors of vertices of a Delta ABC are 4hat(i)-2hat(j), h...

    Text Solution

    |

  16. Given p=3hat(i)+2hat(j)+4hat(k), a=hat(i)+hat(j), b=hat(j)+hat(k), c=h...

    Text Solution

    |

  17. Volume of the parallelopiped having vertices at O-=(0,0,0) , A-=(2,-2...

    Text Solution

    |

  18. If 2veca+ 3vecb-5 vecc=vec0, then ratio in which vecc divides vec...

    Text Solution

    |

  19. If the constant forces 2hati-5hatj+6hatk and -hati+2hatj-hatk act on a...

    Text Solution

    |

  20. If the vectors hat(i)-3hat(j)+2hat(k), -hat(i)+2hat(j) represent the d...

    Text Solution

    |

  21. If |vec(a)|=2,|vec(b)|=3andvec(a),vec(b) are mutually perpendicular, t...

    Text Solution

    |