Home
Class 12
MATHS
Find the shortest distance between the l...

Find the shortest distance between the lines whose vector equations are `vec(r)=hat(i)+2hat(j)+3hat(k)+lamda(hat(i)-3hat(j)+2hat(k))` and `vec(r)=4hat(i)+5hat(j)+6hat(k)+mu(2hat(i)+3hat(j)+hat(k))`.

Text Solution

Verified by Experts

The correct Answer is:
`(3)/(sqrt(19))` units
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    OMEGA PUBLICATION|Exercise Multiple Choice Questions ( MCQs)|32 Videos

  • SAMPLE QUESTION PAPER

    OMEGA PUBLICATION|Exercise QUESTIONS|78 Videos

  • VECTOR ALGEBRA

    OMEGA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS (MCQs) |23 Videos

Similar Questions

Explore conceptually related problems

Find the shortest distance between the lines whose vector equations are : vec(r)=(-2hat(i)+3hat(j)+5hat(k))+lambda(7hat(i)-hat(k)) and vec(r)=4hat(i)+5hat(j)+6hat(k)+mu(2hat(i)+3hat(j)+hat(k))

Find the shortest distance between the lines whose vector equations are : vec(r)=6hat(i)+2hat(j)+2hat(k)+lamda(hat(i)-2hat(j)+2hat(k)) and vec(r)=-4hat(i)-hat(k)+mu(3hat(i)-2hat(j)-4hat(k))

Find the shortest distance between the lines whose vector equations are : vec(r)_(1)=2hat(i)+3hat(j)+4hat(k)+lamda(2hat(i)-hat(j)+hat(k)) vec(r)_(2)=3hat(i)-2hat(j)-hat(k)+mu(3hat(i)+2hat(j)-4hat(k))

Find the shortest distance between the lines vec(r)=(hat(i)+2hat(j)+hat(k))+lamda(hat(i)-hat(j)+hat(k)) and vec(r)=2hat(i)-hat(j)-hat(k)+mu(3hat(i)-hat(j)+hat(k))

Find the shortest distance between the following lines vec(r)=-hat(i)+2hat(j)-hat(k)+lamda(hat(i)+hat(j)-hat(k)) and vec(r)=hat(i)-hat(j)+2hat(k)+mu(-hat(i)+hat(j)+hat(k)) .

Find the shortest distance between the lines vec(r)=hat(i)+2hat(j)+3hat(k)+lamda(2hat(i)+3hat(j)+4hat(k)) and vec(r)=2hat(i)+4hat(j)+5hat(k)+mu(3hat(i)+4hat(j)+4hat(k))

Find the shortest distance between the following lines vec(r)=hat(i)-hat(j)-hat(k)+lamda(hat(i)+hat(j)-hat(k)) and vec(r)=3hat(i)-hat(j)-2hat(k)+mu(-hat(i)+2hat(j)+hat(k))

OMEGA PUBLICATION-THREE DIMENSIONAL GEOMETRY -Questions
  1. Find the angle between the line (x+1)/2 = y/3 = (z-3)/6 and the plane ...

    Text Solution

    |

  2. The vector equation of two lines are vec(r)=hat(i)+2hat(j)+hat(k)+la...

    Text Solution

    |

  3. Find the shortest distance between the lines whose vector equations ar...

    Text Solution

    |

  4. Find the shortest distance between the following two lines vec(r)=(1+2...

    Text Solution

    |

  5. The vector equation of two lines are vec(r)=(1-t)hat(i)+(t-2)hat(j)...

    Text Solution

    |

  6. Find the equation of plane passing through (a,b,c) and parallel to the...

    Text Solution

    |

  7. In the following cases, find the co-ordinates of the foot of the perpe...

    Text Solution

    |

  8. Find the co-ordinates of the foot of perpendicular drawn from the orig...

    Text Solution

    |

  9. Find the length and the foot of the perpendicular from the point (7, 1...

    Text Solution

    |

  10. Find vector equation of line passing through (1,2,3) and perpendicular...

    Text Solution

    |

  11. Find the shortest distance between the lines (x+1)/(7)=(y+1)/(-6)=(...

    Text Solution

    |

  12. Find the co-ordinates of the points where the line through the points ...

    Text Solution

    |

  13. Find the vector equation of the plane which is at a distance of 7 unit...

    Text Solution

    |

  14. Find the cartesian equation of plane vec(r)*(hat(i)+hat(j)-hat(k))=2

    Text Solution

    |

  15. Find the co-ordinates of the foot of the perpendicular drawn from the ...

    Text Solution

    |

  16. Find the equations of the plane that passes through three points : (1,...

    Text Solution

    |

  17. Find the equation of the plane passing through the point ( 1, -1 , 2) ...

    Text Solution

    |

  18. Find the intercepts cut off by the plane 2x+y-z = 5

    Text Solution

    |

  19. Find the vector equation of the plane through the intersection of the ...

    Text Solution

    |

  20. Find the equation of the plane through the intersection of the planes ...

    Text Solution

    |