Home
Class 12
MATHS
Find the volume tetrahedron whose coterm...

Find the volume tetrahedron whose coterminus edges are `7hat(i)+hat(k),2hat(i)+5hat(j)-3hat(k)and 4hat(i)+3hat(j)+hat(k)`.

Text Solution

Verified by Experts

The correct Answer is:
14 cu units.
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Multiple choice question|10 Videos

  • VECTORS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Theory Questions|4 Videos

  • TRIGONOMETRIC FUNCTIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Multiple Choice Questions|12 Videos

Similar Questions

Explore conceptually related problems

The volume of the tetrahedron whose co-terminous edges are hat(j)+hat(k), hat(k)+hat(i), hat(i)+hat(j) is

Find the volume of the parallelopiped whose coterminus edges are : (1) 3hat(i)+5hat(k),4hat(i)+2hat(j)-3hat(k),3hat(i)+hat(j)+4hat(k) (2) bar(a)=hat(i)+hat(j),bar(b)=hat(j)+hat(k),bar(c)=hat(k)+hat(i) (3) 2hat(i)+5hat(j)-4hat(k),5hat(i)+7hat(j)+5hat(k),4hat(i)+5hat(j)-2hat(k) .

Find the altitude of a parallelopiped whose three conterminous edges are verctors A=hat(i)+hat(j)+hat(k), B=2hat(i)+4hat(j)-hat(k) and C=hat(i)+hat(j)+3hat(k) with A and B as the sides of the base of the parallelopiped.

Prove that the volume of the parallelopiped with coterminus edges as bar(a), bar(b), bar(c) is [bar(a),bar(b),bar(c)] and hence find the volume of the parallelopiped with its coterminus edges hat(i)+5hat(j)-4hat(k),5hat(i)+7hat(j)+5hat(k) and 4hat(i)+5hat(j)-2hat(k) .

Find the volume of the parallelopiped whose coterminus edges are given by vectors 2hat(i)+3hat(j)-4hat(k),5hat(i)+7hat(j)+5hat(k)and4hat(i)+5hat(j)-2hat(k) .

The volume of the parallelepiped whose edges are (-12hat(i)+lambdahat(k)), (3hat(j)-hat(k))and (2hat(i)+hat(j)-15hat(k)) is 546 cubic units. Find the value of lambda .

The volume of the paralleloP1ped with co-terminous edges given by the vectors 2hat(i)+5hat(j)-4hat(k), 5hat(i)+7hat(j)+5hat(k), 4hat(i)+5hat(j)-2hat(k) is

If [[hat(i)+4hat(j)+6hat(k), 2hat(i)+ahat(j)+3hat(k), hat(i)+2hat(j)-3hat(k)]]=0 then a=

NAVNEET PUBLICATION - MAHARASHTRA BOARD-VECTORS-Examples for Practics
  1. Express bar(p) as a linear combination of bar(a),bar(b)andbar(c), wher...

    Text Solution

    |

  2. Express the vector bar(a)=9hat(i)+hat(j)+2hat(k) as a linear combinati...

    Text Solution

    |

  3. If bar(a),bar(b),bar(c) are non-zero, non -coplanar vectors, then show...

    Text Solution

    |

  4. If bar(a)+lamdabar(b)+3bar(c),-2bar(a)+3bar(b)-4bar(c),bar(a)-3bar(b)+...

    Text Solution

    |

  5. D, E, F are the midpoints of the sides BC, CA and AB respectively of t...

    Text Solution

    |

  6. Show that if bar(AB)=bar(DC), then the figure ABCD is a parallelogram.

    Text Solution

    |

  7. If G is the centroid of triangleABC and O is any point in the plane of...

    Text Solution

    |

  8. Find [bar(a)bar(b)bar(c)] where : (1) bar(a)=2hat(i)+hat(j)-hat(k),b...

    Text Solution

    |

  9. If bar(a)=hat(i)+hat(j)+hat(k),bar(b)=2hat(i)+qhat(j)+hat(k),hat(c)=ha...

    Text Solution

    |

  10. Show that the vectors hat(i)-hat(j)-6hat(k),hat(i)-3hat(j)+4hat(k)and2...

    Text Solution

    |

  11. Find the volume of the parallelopiped whose coterminus edges are : (...

    Text Solution

    |

  12. Find lamda, if the vectors bar(a)=hat(i)+hat(j)+hat(k),bar(b)=hat(i)-h...

    Text Solution

    |

  13. If bar(a),bar(b),bar(c) are any three vectors, prove that (1) [bar(a)...

    Text Solution

    |

  14. Find the volume of the parallelopiped with segments AB, AC and AD as c...

    Text Solution

    |

  15. Find the volume of the tetrahedron whose vertices are A(3,7,4),B(5,-2,...

    Text Solution

    |

  16. Find the volume tetrahedron whose coterminus edges are 7hat(i)+hat(k),...

    Text Solution

    |

  17. Show that the following sets of points are coplanar : (1) (3,9,4),(0...

    Text Solution

    |

  18. Find the value of x, if the points A(3,2,1),B(4,x,5),C(4,2,2)andD(6,5,...

    Text Solution

    |

  19. If the origin and the points P(2,3,4), Q(1,2,3) and R(x,y,z) are copla...

    Text Solution

    |

  20. If bar(u)=bar(i)-2bar(j)+bar(k),bar(v)=3bar(i)+bar(k)andbar(w)=bar(j)-...

    Text Solution

    |