Home
Class 12
MATHS
A and B are two points. The position vec...

A and B are two points. The position vector of A is 6b-2a. A point P divides the line AB in the ratio 1:2. if a-b is the position vector of P, then the position vector of B is given by

A

7a-15b

B

7a+15b

C

15a-7b

D

15a+7b

Text Solution

Verified by Experts

The correct Answer is:
A
`OP=(1(OB)+2(6b-2a))/(1+2)`

`implies 3(a-b)=OB+12b-4a`
`implies OB=7a-15b`
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|7 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|3 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 3|11 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|19 Videos

Similar Questions

Explore conceptually related problems

If the position vector of p is 3barp+barq and barp divides PQ internally in the ratio 3:4 , the position vector of Q is

bara,barb are position vectors of points A and B. If P divides AB in the ratio 3:1 and Q is the mid-point of AP, then position vectors of Q will be

If the position vector of a point A is vec a + 2 vec b and vec a divides AB in the ratio 2:3 , then the position vector of B, is

The position vector of two points A and B are 6veca+2vecb and veca-3vecb. If point C divides AB in the ratio 3:2 then show that the position vector of C is 3veca-vecb

If a and b are position vector of two points A,B and C divides AB in ratio 2:1, then position vector of C is

barp and barq are position vectors of two points P and Q. The position vectors of a point which divides PQ internally in the ratio 2:5 is

Find the position vector of the point which divides 2vec a-3vec b and 3vec a-2vec b in the ratio 2:3

The position vectors of P and Q are respectively vec a and vec b . If R is a point on vec(PQ) such that vec(PR) = 5 vec(PQ), then the position vector of R, is

ARIHANT MATHS-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
  1. If P and Q are the middle points of the sides BC and CD of the paralle...

    Text Solution

    |

  2. If the figure formed by the four points hati+hatj-hatk,2hati+3hatj,3ha...

    Text Solution

    |

  3. A and B are two points. The position vector of A is 6b-2a. A point P ...

    Text Solution

    |

  4. If three points A,B and C are collinear, whose position vectors are ha...

    Text Solution

    |

  5. If in a triangle AB=a,AC=b and D,E are the mid-points of AB and AC res...

    Text Solution

    |

  6. The sides of a parallelogram are 2hati +4hatj -5hatk and hati + 2hatj ...

    Text Solution

    |

  7. If A, B, C are the vertices of a triangle whose position vectros are v...

    Text Solution

    |

  8. If ABCDEF is a regular hexagon then vec(AD)+vec(EB)+vec(FC) equals :

    Text Solution

    |

  9. ABCDE is a pentagon. Forces AB,AE,DC and ED act at a point. Which forc...

    Text Solution

    |

  10. In a regular hexagon ABCDEF, bar(AB) + bar(AC)+bar(AD)+ bar(AE) + bar(...

    Text Solution

    |

  11. Let us define the length of a vector ahati+bhatj+chatk and |a|+|b|+|c|...

    Text Solution

    |

  12. If a and b are two non-zero and non-collinear vectors then a+b and a-b...

    Text Solution

    |

  13. If |veca+ vecb| lt | veca- vecb|, then the angle between veca and vecb...

    Text Solution

    |

  14. The magnitudes of mutually perpendicular forces a,b and c are 2,10 and...

    Text Solution

    |

  15. If hati-3hatj+5hatk bisects the angle between hata and -hati+2hatj+2ha...

    Text Solution

    |

  16. Let vec a= hat i be a vector which makes an angle of 120^@ with a unit...

    Text Solution

    |

  17. Given three vectors a=6hati-3hatj,b=2hati-6hatj and c=-2hati+21hatj su...

    Text Solution

    |

  18. ' I ' is the incentre of triangle A B C whose corresponding sides are ...

    Text Solution

    |

  19. If vec x andvec y are two non-collinear vectors and a triangle ABC wit...

    Text Solution

    |

  20. If vec xa n d vec y are two non-collinear vectors and a, b, and c ...

    Text Solution

    |