Home
Class 12
MATHS
Find the value of a so that the volume ...

Find the value of a so that the volume of the parallelopiped formed by vectors `hati+ahatj+hatk,hatj+ahatkandahati+hatk` becomes minimum.

A

`-3`

B

3

C

`1//sqrt(3)`

D

`sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE) (INTEGER TYPE)|4 Videos
  • VECTORS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE) (TRUE/ FALSE)|30 Videos
  • VECTORS

    VMC MODULES ENGLISH|Exercise JEE MAIN (ARCHIVE)|60 Videos
  • TRIGONOMETRIC IDENTITIES AND EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|11 Videos

Similar Questions

Explore conceptually related problems

The value of a, such that the volume of the parallelopiped formed by the vectors hati+hatj+hatk, hatj+ahatk and ahati+hatk becomes minimum, is

The value of a so thast the volume of parallelpiped formed by vectors hati+ahatj+hatk, hatj+ahatk, ahati+hatk becomes minimum is (A) sqrt93) (B) 2 (C) 1/sqrt(3) (D) 3

If the volume of parallelopiped formed by the vectors hati+lamdahatj+hatk,hatj+lamdahatk and lamdahati+hatk is minimum then lamda is equal to (1) -(1)/(sqrt(3)) (2) (1)/(sqrt(3)) (3) sqrt(3) (4) -sqrt(3)

Find the volume of the parallelepiped with co-terminous edges 2 hati + hatj - hatk, hati + 2 hatj + 3 hatk and - 3 hati - hatj + hatk

Find the volume of the parallelopiped whose edges are represented by a=2hati-3hatj+4hatk,b=hati+2hatj-hatk and c=3hati-hatj+2hatk .

Find the volume of the parallelopiped, whose three coterminous edges are represented by the vectors hati+hatj+hatk,hati-hatj+hatk,hati+2hatj-hatk .

If the volume of the parallelopiped whose coterminus edges are represented by the vectors 5hati -4hatj +hatk , 4hati+3hatj-lambda hatk and hati-2hatj+7hatk is 216 cubic units, find the value of lambda .

Find the unit vector in the direction of the resultant of vectors hati-hatj+hat3k, 2hati+hatj-2hatk and 2hatj-2hatk

The angle between vectors (hati+hatj+hatk) and (hatj+hatk) is :

Find the value of lamda so that the two vectors 2hati+3hatj-hatk and -4hati-6hatj+lamda hatk are parallel

VMC MODULES ENGLISH-VECTORS -JEE ADVANCED (ARCHIVE)
  1. The edges of a parallelopiped are of unit length and are parallel to ...

    Text Solution

    |

  2. The number of distinct real values of alpha, for which the vectors -la...

    Text Solution

    |

  3. Find the value of a so that the volume of the parallelopiped formed b...

    Text Solution

    |

  4. Let A be vector parallel to line of intersection of planes P1 and P2. ...

    Text Solution

    |

  5. The vector(s) which is /are coplanar with vectors hati +hatj + 2hatk a...

    Text Solution

    |

  6. Let vecu = u(1)hati + u(2)hatj +u(3)hatk be a unit vector in R^(3) a...

    Text Solution

    |

  7. Let PQR be a triangle . Let veca=overline(QR),vecb = overline(RP) and ...

    Text Solution

    |

  8. Let O be the origin and let PQR be an arbitrary triangle. The point S ...

    Text Solution

    |

  9. Let O be the origin and vec(OX) , vec(OY) , vec(OZ) be three unit vec...

    Text Solution

    |

  10. Let O be the origin and vec(OX) , vec(OY) , vec(OZ) be three unit vec...

    Text Solution

    |

  11. The components of a vector veca along and perpendicular to a non-zero ...

    Text Solution

    |

  12. A, B C and D are four points in a plane with position vectors, veca, v...

    Text Solution

    |

  13. Let vecA , vecB and vecC be vectors of legth , 3,4and 5 respectively. ...

    Text Solution

    |

  14. If vecb and vecc are any two mutually perpendicular unit vectors and v...

    Text Solution

    |

  15. Find a unit vector pependicular to the plane determined by the points ...

    Text Solution

    |

  16. the area of the triangle whose vertices are A ( 1,-1,2) , B ( 1,2, -1)...

    Text Solution

    |

  17. Let vec(OA) =veca, vec(OB) = 10veca + 2vecb and vec(OC) =vecb where , ...

    Text Solution

    |

  18. If the vectors ahati+hatj+hatk, hati+bhatj+hatk, hati+hatj+chatk(a!=1,...

    Text Solution

    |

  19. If vecA,vecB,vecC are non-coplanar vectors than ( vecA . vecB xx vecC...

    Text Solution

    |

  20. If |(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^3)|=0 and vectors (1,a,a^2)...

    Text Solution

    |