Home
Class 12
MATHS
Show that the four points A,B,C,D with p...

Show that the four points A,B,C,D with position vectors `veca*vecb*vecc*vecd` respectively, are coplanar if and only if `3veca-2vecb+vecc-2vecd=vec0`.

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 four points A,B,C,D with position vectors veca,vecb,vecc,vecd respectively, such that 3veca-2vecb+5vecc-6vecd=vec0 , are collinear. Also find the position vector of the point of intersection of the lines Ac and BD.

A, B, C and D have position vectors veca, vecb, vecc and vecd , repectively, such that veca-vecb = 2(vecd-vecc) . Then

What is [vecavecbvecc] when veca,vecb,vecc are coplanar ?

Show that points with position vectors 2veca-2vecb+3vecc,-2veca+3vecb-vecc and 6veca-7vecb+7vecc are collinear. It is given that vectors veca,vecb and vecc and non-coplanar.

For any three vectors veca,vecb,vecc show that veca-vecb,vecb-vecc,vecc-veca are coplanar.

If veca,vecb,vecc are coplanar then show that veca+vecb, vecb+vecc and vecc+veca are also coplanar.

Show that the three points veca-2vecb+3vecc, 2veca+3vecb-4vecc and -7vecb+10vecc are collinear.

For non-zero vectors veca, vecb and vecc , |(veca xx vecb) .vecc| = |veca||vecb||vecc| holds if and only if

If non-zero vectors veca and vecb are equally inclined to coplanar vector vecc , then vecc can be

MODERN PUBLICATION-VECTORS-Exercise
  1. If the position vectors of the vertices of a triangle are : vecA=hati+...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Evaluate the product (3 hata-5hatb) cdot(2hata+7hatb)

    Text Solution

    |