Home
Class 12
MATHS
If D is the mid-point of the side B C of...

If `D` is the mid-point of the side `B C` of a triangle `A B C ,` prove that ` vec A B+ vec A C=2 vec A Ddot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ALGEBRA OF MATRICES

    RD SHARMA ENGLISH|Exercise All Questions|410 Videos

  • APPLICATION OF INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|163 Videos

Similar Questions

Explore conceptually related problems

If D and E are the mid-points of sides AB and AC of a triangle A B C respectively, show that vec B E+ vec D C=3/2 vec B Cdot

If D is the mid point of side BC of a triangle ABC such that vec A B+ vec A C=lambda\ vec A D , write the value of lambdadot

If a ,b ,c are the lengths of sides, B C ,C A and A B of a triangle A B C , prove that vec B C+ vec C A+ vec A B= vec O and deduce that a/(sinA)=b/(sinB)=c/(sinC)dot

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

If vec a ,\ vec b ,\ vec c be the vectors represented by the sides of a triangle, taken in order, then prove that vec a+ vec b+ vec c= vec0dot

If A B C D is quadrilateral and E and F are the mid-points of AC and BD respectively, prove that vec A B+ vec A D + vec C B + vec C D =4 vec E Fdot

If veca , vec b and vec c represents three sides of a triangle taken in order prove that veca xx vec b = vec b xx vec c = vec c xx vec a

RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. Show that the points with position vectors vec a-2 vec b+3 vec c ,-2 ...

    Text Solution

    |

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

    Text Solution

    |

  3. If D is the mid-point of the side B C of a triangle A B C , prove that...

    Text Solution

    |

  4. Show that the found points A ,B ,C ,D with position vectors vec a , v...

    Text Solution

    |

  5. Let vec a , vec b , vec c be the position vectors of three distinct p...

    Text Solution

    |

  6. If vec a and vec b are position vectors of points Aa n dB respectivel...

    Text Solution

    |

  7. If vec aa n d vec b are position vectors of Aa n dB respectively, fin...

    Text Solution

    |

  8. If vec c = 3vec a+4vec b and 2vec c =vec a -3vec b, show that (i) vec ...

    Text Solution

    |

  9. Find the position vectors of the points which divide the join of th...

    Text Solution

    |

  10. Let O be the centre of a regular hexagon A B C D E F . Find the sum of...

    Text Solution

    |

  11. For any two vectors vec aa n d vec b , prove that | vec a+ vec b|lt=|...

    Text Solution

    |

  12. IF P1, P2, P3, P4 are points in a plane or space and O is the origin o...

    Text Solution

    |

  13. Using vectors, find the value of lambda such that the points (lambda,...

    Text Solution

    |

  14. If vec a , vec b are any two vectors, then give the geometrical int...

    Text Solution

    |

  15. If vec P O+ vec O Q= vec Q O+ vec O R , show that the point, P ,Q ,R ...

    Text Solution

    |

  16. If the sum of two unit vectors is a unit vector, prove that the mag...

    Text Solution

    |

  17. If vec aa n d vec b are the vectors determined by two adjacent sides ...

    Text Solution

    |

  18. Vectors drawn the origin O to the points A , Ba n d C are respectively...

    Text Solution

    |

  19. If vec aa n d vec b represent two adjacent sides vec A Ba n d vec B ...

    Text Solution

    |

  20. A , B , P, Q and R are five points in a plane. Show that the su...

    Text Solution

    |