Home
Class 12
MATHS
If vec a ,\ vec b ,\ vec c and vec d...

If ` vec a ,\ vec b ,\ vec c` and ` vec d` are the position vectors of points `A , B ,\ C ,\ D` such that no three of them are collinear and ` vec a+ vec c= vec b+ vec d ,\ t h e n\ A B C D` is a a. rhombus b. rectangle c. square d. parallelogram

A

rhombus

B

rectangle

C

square

D

parallelogram

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`vec a + vec c = vec b + vec d `
`rArr vec b - vec a = vec c - vec d and vec d - vec a = vec c - vec b `
`rArr A vec B = D vec C and A vec D = B vec C `
`rArr ABCD ` is a parallelogram.
Promotional Banner

Topper's Solved these Questions

  • ALGEBRA OF VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|30 Videos

  • ALGEBRA OF VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • ALGEBRAIC INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|39 Videos

Similar Questions

Explore conceptually related problems

If vec a , vec b , vec c , vec d are the position vector of point A , B , C and D , respectively referred to the same origin O such that no three of these point are collinear and vec a + vec c = vec b + vec d , than prove that quadrilateral A B C D is a parallelogram.

If vec a , vec b , vec c , vec d are the position vector of point A , B , C and D , respectively referred to the same origin O such that no three of these point are collinear and vec a + vec c = vec b + vec d , than prove that quadrilateral A B C D is a parallelogram.

If vec a ,vec b,vec c and vec d are the position vectors of the points A, B, C and D respectively in three dimensionalspace no three of A, B, C, D are collinear and satisfy the relation 3vec a-2vec b +vec c-2vec d = 0 , then

Let vec a , vec b , vec c , vec d be the position vectors of the four distinct points A , B , C , Ddot If vec b- vec a= vec c- vec d , then show that A B C D is parallelogram.

Let vec a , vec b , vec c , vec d be the position vectors of the four distinct points A , B , C , Ddot If vec b- vec a= vec a- vec d , then show that A B C D is parallelogram.

Let vec a , vec b , vec c , vec d be the position vectors of the four distinct points A , B , C , Ddot If vec b- vec a= vec c- vec a , then show that A B C D is parallelogram.

If vec a ,\ vec b ,\ vec c are position vectors o the point A ,\ B ,\ a n d\ C respectively, write the value of vec A B+ vec B C+ vec A Cdot

If vec a ,\ vec b ,\ vec c are position vectors of the vertices A ,\ B\ a n d\ C respectively, of a triangle A B C ,\ write the value of vec A B+ vec B C+ vec C Adot

vec a , vec b and vec c are the position vectors of points A ,B and C respectively, prove that : vec a× vec b+ vec b× vec c+ vec c× vec a is vector perpendicular to the plane of triangle A B Cdot

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d). (vec b- vec c)!=0,

OBJECTIVE RD SHARMA ENGLISH-ALGEBRA OF VECTORS-Chapter Test
  1. If vec a ,\ vec b ,\ vec c and vec d are the position vectors of p...

    Text Solution

    |

  2. If the vectors vec a =2hati + 3hatj +6hatk and vec b are collinear and...

    Text Solution

    |

  3. If vec a , vec b , vec c are three non-zero vectors (no two of which ...

    Text Solution

    |

  4. Vectors vec aa n d vec b are non-collinear. Find for what value of ...

    Text Solution

    |

  5. If the diagonals of a parallelogram are 3 hati + hatj -2hatk and hati ...

    Text Solution

    |

  6. If ABCD is a quadrilateral, then vec(BA) + vec(BC)+vec(CD) + vec(DA)=

    Text Solution

    |

  7. The points with position vectors 60hati+3hatj,40hati-8hatj, ahati-52ha...

    Text Solution

    |

  8. If ABCDEF is a regualr hexagon, then vec(AC) + vec(AD) + vec(EA) + ve...

    Text Solution

    |

  9. In a regular hexagon ABCDEF, vec(AB)+vec(AC)+vec(AD)+vec(AE)+vec(AF)=k...

    Text Solution

    |

  10. If P, Q , R are the mid-points of the sides AB, BC and CA of Delta AB...

    Text Solution

    |

  11. If G is the centroid of the DeltaABC and if G' is the centroid of anot...

    Text Solution

    |

  12. In a quadrilateral ABCD, vec(AB) + vec(DC) =

    Text Solution

    |

  13. If ABCDE is a pentagon, then vec(AB) + vec(AE) + vec(BC) + vec(DC) +...

    Text Solution

    |

  14. If ABCD is a parallelogram, then vec(AC) - vec(BD) =

    Text Solution

    |

  15. In a Delta ABC, " if " vec(AB) = hati - 7hatj + hatk and vec(BC) = 3 ...

    Text Solution

    |

  16. If vectors vec(AB) = -3hati+ 4hatk and vec(AC) = 5hati -2hatj+4hatk ar...

    Text Solution

    |

  17. The position vectors of P and Q are respectively vec a and vec b . If ...

    Text Solution

    |

  18. If the points whose position vectors are 2hati + hatj + hatk , 6hati -...

    Text Solution

    |

  19. The ratio in which hati + 2 hatj + 3 hatk divides the join of -2hati ...

    Text Solution

    |

  20. If OACB is a parallelogrma with vec( OC) = vec(a) and vec( AB) = vec(...

    Text Solution

    |

  21. The position vectors of the points A, B, C are 2 hati + hatj - hatk , ...

    Text Solution

    |