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

A. 7a-15b

B

B. 7a+15b

C

C. 15a-7b

D

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 VECTOR ALGEBRA EXERCISES 1: Single Option Correct Type Questions|1 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|7 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)|18 Videos

Similar Questions

Explore conceptually related problems

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

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

Position vector of a point P is vectors whose initial point is origin.

The position vector of the point which divides the join of points with position vectors veca+vecb and 2veca-vecb in the ratio 1:2 is

The position vector of the point which divides the join of points with position vectors vec a+vec b and 2vec a-vec b inthe ratio 1: 2 is

The position vector of the point which divides the join of points 2 vec a -3 vec b and vec a+vec b in the ratio 3: 1 is

Find the position vector of a point, which divides the join of the points with position vectors veca-2vecb and 2 veca + vecb externally in the ratio 2 : 1 .

The position vector of a point C with respect to B is hat i +hat j and that of B with respect to A is hati-hatj . The position vector of C with respect to A is

The position vector of the point which divides the join of points 2veca-3vecb and veca+vecb in the ratio 3:1 is

If the position vectors of the points A and B are hati+3hatj-hatk and 3hati-hatj-3hatk , then what will be the position vector of the mid-point of AB

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 two adjacent sides of a parallelogram are 2hati+4hatj-5hatk and ha...

    Text Solution

    |

  7. If A,B and C are the vertices of a triangle with position vectors vec(...

    Text Solution

    |

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

    Text Solution

    |

  9. Find the discriminant of the quadratic equation x^2+3x+2

    Text Solution

    |

  10. In a regular hexagon ABCDEF, prove that AB+AC+AD+AE+AF=3AD.

    Text Solution

    |

  11. Find the dot product of the vector 2hati+3hatj+1hatk and 1hati+2hatj+3...

    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. Find the discriminant of the quadratic equation x^2+5x+4=0 and also fi...

    Text Solution

    |

  17. Given three vectors vec a=6 hat i-3 hat j , vec b=2 hat i-6 hat ja ...

    Text Solution

    |

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

    Text Solution

    |

  19. If vecx and vecy are two non-collinear vectors and ABC is a triangle w...

    Text Solution

    |

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

    Text Solution

    |