Home
Class 12
MATHS
If D and E are the mid-points of sides A...

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`

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 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

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

If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n dB D respectively, prove that vec A B+ vec A D + vec C B + vec C D =4 vec E Fdot

If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n dB D respectively, prove that vec A B+ vec A D + vec C B + vec C D =4 vec E Fdot

If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n dB D respectively, prove that vec A B+ vec A D + vec C B + vec C D =4 vec E Fdot

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 D ,\ E ,\ F are the mid points of the side B C ,\ C A and A B respectively of a triangle ABC, write the value of vec A D+ vec B E+ vec C Fdot

If D, E, F are respectively the mid-points of AB, AC and BC respectively in a Delta ABC, " then " vec (BE) + vec(AF) =

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 .

RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. If the points with position vectors 60 hat i+2 hat j , 40 hat i-8 hat ...

    Text Solution

    |

  2. If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n d...

    Text Solution

    |

  3. If D and E are the mid-points of sides AB and AC of a triangle A B C r...

    Text Solution

    |

  4. If G is the centroid of a triangle A B C , prove that vec G A+ vec G ...

    Text Solution

    |

  5. Prove using vectors: Medians of a triangle are concurrent.

    Text Solution

    |

  6. Points L, M, N divide the sides BC, CA, AB of ABC in the ratio 1:4, 3:...

    Text Solution

    |

  7. Prove using vectors: The diagonals of a quadrilateral bisect each o...

    Text Solution

    |

  8. Show that the line segments joining the mid-points of opposite side...

    Text Solution

    |

  9. Prove that the line segment joining the mid points of two side of a...

    Text Solution

    |

  10. A vector vec r is inclined at equal to O X ,O Ya n dO Zdot If the mag...

    Text Solution

    |

  11. A vector vec r has length 21 and its direction ratios are proport...

    Text Solution

    |

  12. If vec a and vec b are non-collinear vectors and vectors vecalpha=(x...

    Text Solution

    |

  13. A B C D is a parallelogram. E ,F are mid-points of B C ,C D respective...

    Text Solution

    |

  14. If a\ a n d\ b ar non collinear vector such that x1 vec a+y1 vec b=x2 ...

    Text Solution

    |

  15. Show that the vectors a, b, c given by vec a= hat i+2 hat j+3 hat k ,...

    Text Solution

    |

  16. A vector vec O P is inclined to O X at 50^0 and O Y at 60^0 . Find th...

    Text Solution

    |

  17. If a vector makes angles alpha,beta,gamma. with . OX ,O Ya n dO Z ...

    Text Solution

    |

  18. A B C D is a parallelogram. If L and M are the mid-points of B C and D...

    Text Solution

    |

  19. Find a unit vector in the direction of the resultant of the vectors...

    Text Solution

    |

  20. Find the position vector of the mid-point of the vector joining the...

    Text Solution

    |