Home
Class 12
MATHS
If hati+hatj+hatk, 2hati+5hatj, 3hati+2h...

If `hati+hatj+hatk, 2hati+5hatj, 3hati+2hatj-3hatk` and `hati-6hatj-hatk` are the position vectors of points A, B, C and D respectively, then find the angle between AB and CD. Deduce that AB and CD are collinear.

Promotional Banner

Topper's Solved these Questions

  • VECTORS

    MODERN PUBLICATION|Exercise Exercise|500 Videos

  • UNIT TEST-4

    MODERN PUBLICATION|Exercise EXERCISE|13 Videos

Similar Questions

Explore conceptually related problems

If veca=-2hati+3hatj+5hatk,vecb=hati+2hatj+3hatkandvecc=7hati-hatk are position vectors of three points A, B, C respectively, prove that A, B, C are collinear.

If a=3hati-2hatj+hatk,b=2hati-4hatj-3hatk and c=-hati+2hatj+2hatk , then a+b+c is

If the vectors 6hati-2hatj+3hatk,2hati+3hatj-6hatk and 3hati+6hatj-2hatk form a triangle, then it is

Show that the vectors 2hati-3hatj+4hatk and -4hati+6hatj-8hatk are collinear.

If the vectors 2hati-hatj+hatk,hati+2hatj-3hatk and 3hati+ahatj+5hatk are coplanar, the prove that a=-4.

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk are coplanar.

If the position vectors of A and B respectively hati+3hatj-7hatk and 5 hati-2hatj+4hatk , then find AB

Show that the points : A(-2hati+3hatj+5hatk), B(hati+2hatj+3hatk) and C(7hati-hatk) are collinear.

If theta is the angle between the vectors a=2hati+2hatj-hatk and b=6hati-3hatj+2hatk , then

MODERN PUBLICATION-VECTORS-Exercise
  1. Consider A(2,3,4),B(4,3,2) and C(5,2,-1) be any three points. Find the...

    Text Solution

    |

  2. Dot-product of a vector with vectors 3hati-5hatk,2hati+7hatj and hati+...

    Text Solution

    |

  3. If hati+hatj+hatk, 2hati+5hatj, 3hati+2hatj-3hatk and hati-6hatj-hatk ...

    Text Solution

    |

  4. If vecalpha=3hati+4hatj+5hatk and vecbeta=2hati+hatj-4hatk, then expre...

    Text Solution

    |

  5. Prove that the perpendicular from the vertices to the opposite sides (...

    Text Solution

    |

  6. Prove that in a right angled triangle the mid-point of the hypotenuse ...

    Text Solution

    |

  7. If two medians of a triangle are equal, prove that the triangle is iso...

    Text Solution

    |

  8. Which of the following statements are True or False : If the diagonals...

    Text Solution

    |

  9. Prove that sum of squares of the diagonals of a parallelogram is equal...

    Text Solution

    |

  10. In any DeltaABC prove by vectors that a^2=b^2+c^2-2 bc cos A.

    Text Solution

    |

  11. In any DeltaABC prove by vectors that b^2=c^2+a^2-2 ca cos B.

    Text Solution

    |

  12. In any triangle ABC, then by vectors, prove that : c^2=a^2+b^2-2ab cos...

    Text Solution

    |

  13. Prove that, in any triangle ABC, cos B=(c^2+a^2-b^2)/(2ca).

    Text Solution

    |

  14. With the help of vector method, prove that,cosA=(b^2+c^2-a^2)/(2bc)

    Text Solution

    |

  15. In any triangle ABC, then by vectors, prove that : a=b cos C+c cos B.

    Text Solution

    |

  16. Use vectors to prove that in triangleABC : b=c cos A+a cos C.

    Text Solution

    |

  17. Using vector method prove that cos(A-B)=cosAcosB+sinAsinB

    Text Solution

    |

  18. In any triangle ABC, show that AB^(2)+AC^(2)=2(AD^(2)+BD^(2)) wher...

    Text Solution

    |

  19. Prove that any two edges in a regular tetrahedron are perpendicular.

    Text Solution

    |

  20. In each problem, find the work done by a force vecF acting on a partic...

    Text Solution

    |