Home
Class 12
MATHS
If A=(0,1)B=(1,0),C=(1,2),D=(2,1) , prov...

If `A=(0,1)B=(1,0),C=(1,2),D=(2,1)` , prove that ` vec A B= vec C Ddot`

Text Solution

Verified by Experts

Given,
`A=(0,1), B=(1,0),C=(1,2),D=(2,1)`
thus,
`AB=(1−0)hati+(0−1)hatj=hati−hatj `
and,
` CD=(2−1)hati+(1−2)hatj=hati−hatj`
So, `AB=CD`
Promotional Banner

Topper's Solved these Questions

  • ALGEBRA OF MATRICES

    RD SHARMA|Exercise Solved Examples And Exercises|410 Videos

  • APPLICATION OF INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|118 Videos

Similar Questions

Explore conceptually related problems

If A=(1,0,1), B=(0,-1,0), C=(-1,0,1), D=(0,1,-1) then angle between vec(AB) and vec(CD) is (A) pi/6 (B) pi/4 (C) pi/3 (D) pi/2

If vec A=(1,1,1),vec C=(0,1,-1) are given vectors,then prove that a vector vec B satisfying the equations vec A xxvec B=vec C and vec A*vec B=3 is ((5)/(3),(2)/(3),(2)/(3))

If vec(a)=(2,1,-1), vec(b)=(1,-1,0), vec(c)=(5, -1,1) , then what is the unit vector parallel to vec(a)+vec(b)-vec(c) in the opposite direction ?

If vec a=(-1,1,2);vec b=(2,1,-1);vec c=(-2,1,3) then the angle between 2vec a-vec c and vec a+vec b is

If vec(a)= (2, 1, -1), vec(b) = (1, -1, 0), c= (5, -1, 1) , then what is the unit vector parallel to vec(a) +vec(b)- vec(c ) in the oppoiste direction?

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

If vec(a), vec(b), vec(c ) are three vectors such that vec(a)xx vec(b)=vec(c ), vec(b)xx vec(c )=vec(a) , prove that vec(a), vec(b), vec(c ) are mutually at right angles and |vec(b)|=1, |vec(c )|=|vec(a)| .

If vec a + vec b + vec c = 0, prove that (vec a xx vec b) = (vec b xx vec c) = (vec c xx vec a)

Let vec a=hat i+hat j+hat k,vec b=hat i and hat c=c_(1)hat i+c_(2)hat j+c_(3)hat k. Then,(1) If c_(1)=1 and c_(2)=2, find c_(3) which makes vec a,vec b and vec c coplanar.(2) If c_(2)=-1 and c_(3)=1, show that no value of c_(1) can make vec a,vec b and vec c coplanar.

If vec(a), vec(b), vec(c ) are three vectors such that vec(a)+vec(b)+vec(c )=0 , then prove that : vec(a)xx vec(b)=vec(b)xx vec(c )=vec(c )xx vec(a) and hence, show that [vec(a)vec(b)vec(c )]=0 .

RD SHARMA-ALGEBRA OF VECTORS-Solved Examples And Exercises
  1. If vec aa n d vec b are two non-collinear vectors, show that point...

    Text Solution

    |

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

    Text Solution

    |

  3. If A=(0,1)B=(1,0),C=(1,2),D=(2,1) , prove that vec A B= vec C Ddot

    Text Solution

    |

  4. Show that the points with position vectors vec a-2 vec b+3 vec c ,-2 ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. If vec aa n d vec b are position vectors of points Aa n dB respective...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. If vec a , vec b are any two vectors, then give the geometrical in...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |