Home
Class 12
MATHS
If the position vectors of the vertices ...

If the position vectors of the vertices of a triangle are : `vecA=hati+2hatj+3hatk, vecB=2hati+3hatj+hatk, vecC=3hati+hatj+2hatk`, show that the triangle is an equilateral one.

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

Show that the following vectors are coplanar : veca=hati-2hatj+3hatk,vecb=-2hati+3hatj-4hatk and vecc=hati-3hatj+5hatk .

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

The sum of the vectors veca=hati-3hatk, vecb=2hatj-hatk,vecc=2hati-3hatj+2hatk is 3hati-hatj-2hatk .

Show that the vectors veca=hati-2hatj+3hatk,vecb=-2hati+3hatj-4hatk and vecc=hati-3hatj+5hatk are coplanar.

MODERN PUBLICATION-VECTORS-Exercise
  1. Show that the following vectors are coplanar : 2hati-hatj+hatk,hati-3h...

    Text Solution

    |

  2. Show that the points A(3,-2,1),B(1,-3,5),C(2,1,-4) do not form a right...

    Text Solution

    |

  3. If the position vectors of the vertices of a triangle are : vecA=hati+...

    Text Solution

    |

  4. If veca = hati + hatj+hatk, vecb = 2hati-hatj+3hatk and vecc = hati-2h...

    Text Solution

    |

  5. Show that the four points A,B,C,D with position vectors veca*vecb*vecc...

    Text Solution

    |

  6. Show that the four points P,Q,R,S with position vectors vecp,vecq,vecr...

    Text Solution

    |

  7. Prove that the necessary and sufficient condition for three vectors ve...

    Text Solution

    |

  8. If veca,vecb,vecc,vecd respectively, are position vectors representing...

    Text Solution

    |

  9. If Q is the point of intersection of the medians of a triangle ABC, pr...

    Text Solution

    |

  10. G is the centroid of a triangle ABC, show that : vec(GA)+vec(GB)+vec(G...

    Text Solution

    |

  11. Let veca,vecb,vecc,vecd be the position vectors of the four distinct p...

    Text Solution

    |

  12. Show that the line joining any vertex of a parallelogram to the mid-po...

    Text Solution

    |

  13. Prove that the figure formed by joining the mid-points of the pairs of...

    Text Solution

    |

  14. Show that if P,A,B are any three points, then lambda vec(PA)+mu vec(PB...

    Text Solution

    |

  15. Obtain the dot product of the vectors : veca=veci-hatj+hatk and vecb=v...

    Text Solution

    |

  16. Write the magnitude of a vector veca in terms of dot product.

    Text Solution

    |

  17. If veca=7hati+hatj-4hatk and vecb=2hati+6hatj+3hatk find the projectio...

    Text Solution

    |

  18. Let veca=2hati+3hatj+2hatk and vceb=hati+2hatj+hatk. Find the projecti...

    Text Solution

    |

  19. Find the projection of the vector hati-hatj on the vector hati+hatj.

    Text Solution

    |

  20. Find veca.vecb If veca=3hati-hatj+2hatk and vecb=2hati+3hatj+3hatk

    Text Solution

    |