Home
Class 12
MATHS
Find the position vector of the mid poin...

Find the position vector of the mid point of the vector joining the points `P(2,3,4)a n d\ Q(4,1,-2)dot`

Text Solution

AI Generated Solution

To find the position vector of the midpoint of the vector joining the points \( P(2, 3, 4) \) and \( Q(4, 1, -2) \), we can follow these steps: ### Step 1: Write the position vectors of points P and Q. The position vector of point \( P \) can be expressed in terms of unit vectors \( \hat{i}, \hat{j}, \hat{k} \): \[ \mathbf{p} = 2\hat{i} + 3\hat{j} + 4\hat{k} ...
Promotional Banner

Topper's Solved these Questions

  • ALGEBRA OF MATRICES

    RD SHARMA ENGLISH|Exercise All Questions|410 Videos
  • APPLICATION OF INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|163 Videos

Similar Questions

Explore conceptually related problems

Find the position vector of the mid point of the vector joining the points P(2, 3, 4) and Q(4, 1, 2) .

Write the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q (4, 1,-2).

Find the position vector of the mid-point of the vector joining the points P(2 hat i-3 hat j+4 hat k"")a n d"Q"(4 hat i+ hat j-2 hat k)dot

Find the equation of the line joining the points (-1,3)a n d\ (4,-2)dot

Find the position vector of the mid point of the line segment A B ,\ where A is the point (3, 4, -2) and B is the point (1, ,2 4).

Find the co-ordinates of the mid point of the line segment joining the points P (4, -6) and (-2, 4).

Find the direction cosines of the vector joining the points A(1,2,-3)a n d B(-1,-2,1), directed from Aa n dBdot

Find the direction cosines of the vector joining the points A(1, 2, -3) and B(-1, -2, 1) directed from A to B .

Find the position vectors of the points which divide the join of the points 2 vec a-3 vec ba n d3 vec a-2 vec 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)=2veca+vecb and vec(OQ)=veca-2vecb , respectively in the ratio 1:2 internally and externally.

RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. Find the unit vector in the direction of vector vec P Q , where P a...

    Text Solution

    |

  2. Show that the points A(2 hat i- hat j+ hat k), B( hat i-3 hat j-5 h...

    Text Solution

    |

  3. Find the position vector of the mid point of the vector joining the ...

    Text Solution

    |

  4. Find the value of x for which x\ ( hat i+ hat j+ hat k) is a unit vect...

    Text Solution

    |

  5. If vec a= hat i+ hat j+ hat k , vec b=4 hat i-2 hat j+3 hat k and ve...

    Text Solution

    |

  6. If vec a= hat i+ hat j+ hat k ,\ vec b=2 hat i- hat j+3 hat k\ a n d...

    Text Solution

    |

  7. Two vectors hat j + hat k and 3 hat i - hat j + 4 hat k represents t...

    Text Solution

    |

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

    Text Solution

    |

  9. If a\ a n d\ b ar non collinear vector such that x1 vec a+y1 vec b=x2 ...

    Text Solution

    |

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

    Text Solution

    |

  11. Show that the three points A(-2, 3,5); B(1, 2, 3) and C(7, 0, -1) are ...

    Text Solution

    |

  12. The position vectors of the points P ,\ Q ,\ R are hat i+2 hat j+3 ha...

    Text Solution

    |

  13. Show that the point A ,B ,C with position vectors vec a-2 vec b...

    Text Solution

    |

  14. If a ,\ b ,\ c are non coplanar vectors prove that the points having t...

    Text Solution

    |

  15. If a ,\ b ,\ c are non coplanar vectors prove that the points having t...

    Text Solution

    |

  16. Prove that the points having position vectors hat i+2 hat j+3 hat k ,...

    Text Solution

    |

  17. If the points with position vectors 10 hat i+3 hat j ,12 hat i-5 ha...

    Text Solution

    |

  18. If vec a , vec b are two non-collinear vectors, prove that the poi...

    Text Solution

    |

  19. If vec A O+ vec O B= vec B O+ vec O C , prove that A , B , C are coll...

    Text Solution

    |

  20. If the points A(m ,-1),\ B(2,1)a n d\ C(4,5) are collinear find the va...

    Text Solution

    |