Home
Class 12
MATHS
Find the position vector of a point R wh...

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are `P(2veca + vecb)` and `Q(veca-3vecb)` externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.

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

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are P(veci+2vecj-veck) and Q(-veci+vecj+veck) respectively, in the ratio 2 : 1, externally.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are P(veci+2vecj-veck) and Q(-veci+vecj+veck) respectively, in the ratio 2 : 1, internally.

Find the position vector of a point R which divides the line joining two points P (2 vec a+ vecb) and Q (vec a-3 vec b) externally in the ratio 1 : 2. Also, show that P is the middle point of the line segment RQ.

The position vector of the point which divides the join of points with position vectors veca+vecb and 2veca-vecb in the ratio 1:2 is

Find the position vector of a point, which divides the join of the points with position vectors veca-2vecb and 2 veca + vecb externally in the ratio 2 : 1 .

MODERN PUBLICATION-VECTORS-Exercise
  1. Consider two points P and Q with position vectors vec(OP) = 3veca-2vec...

    Text Solution

    |

  2. Consider two points P and Q with position vectors vec(OP) = 3veca-2vec...

    Text Solution

    |

  3. Find the position vector of a point R which divides the line joining t...

    Text Solution

    |

  4. Show that the following points are collinear : A(-2,1),B(-5,-1),C(1,3)...

    Text Solution

    |

  5. Show that the following points are collinear : A(1,2,7),B(2,6,3),C(3,1...

    Text Solution

    |

  6. If veca=-2hati+3hatj+5hatk,vecb=hati+2hatj+3hatkandvecc=7hati-hatk are...

    Text Solution

    |

  7. Show that the following vectors are coplanar : hati-hatj+hatk,6hati-ha...

    Text Solution

    |

  8. Show that the following vectors are coplanar : 3hati-2hatj+4hatk,6hati...

    Text Solution

    |

  9. Show that the following vectors are coplanar : 2hati-hatj+hatk,hati-3h...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |