Home
Class 12
MATHS
A B C D is a parallelogram. If L and M a...

`A B C D` is a parallelogram. If `L` and `M` are the mid-points of `B C` and `D C` respectively, then express ` vec A L` and `vec A M` in terms of ` vec A B` and `vec A D` . Also, prove that ` vec A L+ vec A M=3/2 vec A 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

A B C D is a parallelogram. If La n dM are the mid-points of B Ca n dD C respectively, then express vec A La n d vec A M in terms of vec A Ba n d vec A D . Also, prove that vec A L+ vec A M=3/2 vec A Cdot

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 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 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

A B C D E is pentagon, prove that vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

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

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0 vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0 vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0

RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. A vector vec O P is inclined to O X at 50^0 and O Y at 60^0 . Find th...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. Show that the line joining one vertex of a parallelogram to the mid...

    Text Solution

    |

  7. Let vec a , vec b, vec c be three non-zero vectors such that any two ...

    Text Solution

    |

  8. If vec a , vec b are the position vectors of the points (1,-1),(-2,m...

    Text Solution

    |

  9. Find the position vector of a point A in space such that vec O A is i...

    Text Solution

    |

  10. Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6)a n d D(2,-5,1...

    Text Solution

    |

  11. Prove that the lines joining the vertices of a tetrahedron to the ce...

    Text Solution

    |

  12. Find a vector vec r of magnitude 3sqrt(2)u n i t s which makes an an...

    Text Solution

    |

  13. Let vec a= hat i+2 hat ja n d vec b=2 hat i+ hat jdoti s |vec a|=| ve...

    Text Solution

    |

  14. Three vectors of magnitude a ,2a ,3a meet in a point and their directi...

    Text Solution

    |

  15. Show that the vectors vec a-2 vec b+3 vec c , vec a-3 vec b+5 vec ca ...

    Text Solution

    |

  16. Find the angles at which the vector 2 hat i- hat j+2 hat k is inclined...

    Text Solution

    |

  17. Prove that four points 2 vec a+3 vec b- vec c , vec a-2 vec b+3 vec ...

    Text Solution

    |

  18. Find the direction cosines of the vector joining the points A(1,2,-...

    Text Solution

    |

  19. If vec aa n d vec b are two non-collinear vectors, show that points...

    Text Solution

    |

  20. If the position vector vec a of a point (12 ,n) is such that | vec a|...

    Text Solution

    |