Home
Class 12
MATHS
Find the position vector of a point whic...

Find the position vector of a point which divides the join of points with position vectors ` vec a-2 vec b` and `2 vec a+ vec b` externally in the ration 2:1.

Text Solution

Verified by Experts

The correct Answer is:
`=3vec(a)+4vec(b)`
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise Questions From NCERT Exemplar (Example)|3 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (a) Short Answer Type Questions|21 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise CHAPTER TEST 10|12 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

Find the position vector of a point which divides the join of points with position vectors vec a-2vec b and 2vec a+vec b externally in the ration 2:1.

Find the position vector of the point, which divides the join of points with position vectors 3vec(a)-2vec(b) and 2vec(a)+3vec(b) in the ratio 2 : 1.

Find the position vector of a point R which divides the line segment joining P and Q whose position vectors are 2vec a+vec b and vec a-4vec b ,externally in the ratio 1:2, also show that P is the midpoint of the line segment RQ.

Find the position vectors of the points which divide the join of the points 2vec a-3vec b and 3vec a-2vec b internally and externally in the ratio 2:3 .

Find the position vector of a point R which divides the line joining the two points P and Q with position vectors vec OP=2vec a+vec b and vec OQ=vec a-2vec b, respectively in the ratio 1:2 internally and externally.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2vec a+vec b) and (vec a-3vec b) respectively,externally in the ratio 1:2. Also,show that P is the mid-point of the line segment RQ.

Write the position vector of a point dividing the line segment joining points A and B with position vectors vec a and vec b externally in the ration 1:4 where vec a=2hat i+3hat j+4hat k and vec b=-hat i+hat j+hat k

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

Find the position vector of R, which divides the line joining two points P(2vec(a)+vec(b)) and Q(vec(a)-3vec(b)) externally in the ratio 1 : 2. Also show that P is the middle point of the segment RQ.

The position vector of a midpoint lying on the line joining the points whose position vectors are vec i+vec j-vec k and vec i-vec j+vec k is

MODERN PUBLICATION-VECTOR ALGEBRA -Frequently Asked Questions (Example)
  1. Find the position vector of a point which divides the join of points w...

    Text Solution

    |

  2. The two vectors hat j+ hat k and 3 hat i- hat j+4 hat k represent the...

    Text Solution

    |

  3. If vec(a)=4hat(i)-hat(j)+hat(k) and vec(b)=2hat(i)-2hat(j)+hat(k), the...

    Text Solution

    |

  4. Find the vector joining the points P(2, 3, 0) and Q(-1,-2,-4) directed...

    Text Solution

    |

  5. Write the direction ratios of the vector -> a= hat i+ hat j-2 hat k a...

    Text Solution

    |

  6. Find the unit vector in the direction of the sum of the vectors : v...

    Text Solution

    |

  7. Find a vector of magnitude 5 units, and parallel to the resultant of ...

    Text Solution

    |

  8. Prove that if vec(u)=u(1)hat(1)hat(i)+u(2)hat(j) and vec(v)=v(1)hat(i)...

    Text Solution

    |

  9. Find the value of ' p ' for which the vectors 3 hat i+2 hat j+9 hat k\...

    Text Solution

    |

  10. Show that the points, A, B and C having position vectors (2hat(i)-hat(...

    Text Solution

    |

  11. The position vectors of A, B, C are 2hat(i)+hat(j)-hat(k), 3hat(i)-2ha...

    Text Solution

    |

  12. Prove that the four points having position vectors are coplanar: 2 hat...

    Text Solution

    |

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

    Text Solution

    |

  14. Find the magnitude of each of the two vectors veca and vec b having th...

    Text Solution

    |

  15. If vec(a) and vec(b) are perpendicular vectors such that |vec(a)+vec(b...

    Text Solution

    |

  16. Find the projection of the vector hat i+3 hat j+7 hat k on the vector...

    Text Solution

    |

  17. Find lambda, when the projection of vec a=lambda hat i+ hat j+4 hat k...

    Text Solution

    |

  18. If vec a and vec b are two unit vectors such that vec a+ vec b is a...

    Text Solution

    |

  19. Find | vec x| , if for a unit vector vec a ,\ ( vec x-\ vec a)dot( v...

    Text Solution

    |

  20. If ā,b,c are three vectors such that |veca |= 5, |vecb| = 12 and | ...

    Text Solution

    |