Home
Class 12
MATHS
The position vectors of the four angu...

The position vectors of the four angular points of a tetrahedron are `A( hat j+2 hat k),B(3 hat i+ hat k), C(4 hat i+3 hat j+6 hat k)a n dD(2 hat i+3 hat j+2 hat k)dot` Find the volume of the tetrahedron `A B C Ddot`

Text Solution

Verified by Experts

The correct Answer is:
6
Promotional Banner

Topper's Solved these Questions

  • VECTOR

    MOTION|Exercise EXERCISE - 4 ( LEVEL -I)|36 Videos

  • VECTOR

    MOTION|Exercise EXERCISE - 4 ( LEVEL-II)|41 Videos

  • VECTOR

    MOTION|Exercise EXERCISE - 2 ( LEVEL -II)|15 Videos

  • TRIGONOMETRIC EQUATION

    MOTION|Exercise EXERCISE 4|10 Videos

Similar Questions

Explore conceptually related problems

The position vectors of the four angular points of a tetrahedron are A(hat j+2hat k),B(3hat i+hat k),C(4hat i+3hat j+6hat k) and D(2hat i+3hat j+2hat k) Find the volume of the tetrahedron ABCD.

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i-3 hat k) are collinear.

underset with a = 2hat i + hat j-3hat k, vec b = -hat i + hat j + 2hat k, vec c = 4hat i + 3hat k

Find the area of the rriangle formed by the tips of the vectors, vec a= (2 hat I - hat j+ 3 hat k), vec b= 4 hat I + 3 hat j-hat k , vec C= 3 hat I - hat j + 2 hat k .

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

Show that the points A(-2hat i+3hat j+5hat k),B(hat i+2hat j+3hat k) and C(7hat i-hat k) are collinear.

If vec a= hat i+ hat j+ hat k , vec b=2 hat i- hat j+3 hat k a n d vec c= hat i-2 hat j+ hat k find a unit vector parallel to 2 vec a- vec b+3 vec cdot

If the vertices of a tetrahedron have the position vectors vec 0,hat i+hat j,2hat j-hat k and hat i+hat k then the volume of the tetrahedrom is

Show that the four points A,B,C and D with position vectors 4hat i+5hat j+hat k,-(hat j+hat k),3hat j+9hat j+4hat k and 4(-hat i+hat j+hat k) respectively are coplanar.

The position vectors of the points P and Q are 5 hat i+7 hat j- 2 hat k and -3 hat i+3 hat j+6 hat k respecively. The vector vec A=3 hat i-hat j+hat k passes through the point P and the vector vec B=-3 hat i+2 hat j+4 hat k passes through the point Q. A third vector 2 hat i+7 hat j- 5hat k intersects vectors vec A and vec B . Find the position vectors of the points of intersection

MOTION-VECTOR -EXERCISE - 3
  1. The position vectors of the angular points of a tetrahedron are A(3 ha...

    Text Solution

    |

  2. Show that the four points with position vectors4 hat i+8 hat j+12 hat ...

    Text Solution

    |

  3. Examine for coplanarity of the following sets of points 3vec(a) + 2...

    Text Solution

    |

  4. The length of the edge of the regular tetrahedron DABC is 'a'. Point E...

    Text Solution

    |

  5. The position vectors of the four angular points of a tetrahedron ar...

    Text Solution

    |

  6. The position vectors of the four angular points of a tetrahedron ar...

    Text Solution

    |

  7. The position vectors of the four angular points of a tetrahedron ar...

    Text Solution

    |

  8. The position vectors of the four angular points of a tetrahedron ar...

    Text Solution

    |

  9. ABCD is a tetrahedron with pv's of its angular point as A(-5, 22, 5); ...

    Text Solution

    |

  10. Let vec(a) = hat(i) + 2hat(j) + 3hat(k) , vec(b) = 2hat(i) + hat(j) ...

    Text Solution

    |

  11. Let vec(a) = hat(i) + 2hat(j) + 3hat(k) , vec(b) = 2hat(i) + hat(j) ...

    Text Solution

    |

  12. Are the following set of vectors linearly independent? vec(a) = h...

    Text Solution

    |

  13. Are the following set of vectors linearly independent? vec(a) = - 2...

    Text Solution

    |

  14. the resultant of two vectors vec(a) & vec(b) is perpendicular to ve...

    Text Solution

    |

  15. Given three points on the xy plane on O(0, 0), A(1, 0) and B(–1, 0). P...

    Text Solution

    |

  16. Vector vec O A= hat i+2 hat j+2 hat k turns through a right angle ...

    Text Solution

    |

  17. If p vec x +( vec x xx vec a )= vec b ;(p!=0) prove that & vecx...

    Text Solution

    |

  18. Given two orthogonal vectors vec(A) and vec(B) each of length unity ...

    Text Solution

    |

  19. Given two orthogonal vectors vec(A) and vec(B) each of length unity ...

    Text Solution

    |

  20. Which of the following statements is false ?

    Text Solution

    |