Home
Class 12
MATHS
The vector equation of two lines are ...

The vector equation of two lines are
`vec(r)=(1-t)hat(i)+(t-2)hat(j)+(3-2t)hat(k)` and `vec(r)=(s+1)hat(i)+(2s-1)hat(j)-(2s-1)hat(j)-(2s+1)hat(k)`
Find the shortest distance between these lines.

Text Solution

Verified by Experts

The correct Answer is:
`(8)/(sqrt(29))` 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 vector equation of plane that contains the lines vec(r)=(hat(i)+hat(j))+s(hat(i)+2hat(j)-hat(k)) and vec(r)=(hat(i)+hat(j))+t(-hat(i)+hat(j)-2hat(k))

Determine whether the lines vec(r)=3hat(i)-hat(j)+lamda(3hat(i)+hat(k)) and vec(r)=hat(i)-hat(j)+mu(2hat(i)+hat(j)-2hat(k)) intersect or not

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

Determine whether the following pair of lines intersect vec(r)=hat(i)-hat(j)+lamda(2hat(i)-hat(k)) and vec(r)=(2hat(i)-hat(j))+mu(hat(i)-hat(j)-hat(k))

Find the angle between the following planes vec(r)*(hat(i)+hat(j)-2hat(k))=3 and vec(r)*(2hat(i)-2hat(j)+hat(k))=2

Find the angle between the following planes vec(r)*(3hat(i)-4hat(j)+5hat(k))=0 and vec(r)*(2hat(i)-hat(j)-2hat(k))=0

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

OMEGA PUBLICATION-THREE DIMENSIONAL GEOMETRY -Questions
  1. Find the shortest distance between the lines whose vector equations ar...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Find the equation of the plane passing through the line of intersectio...

    Text Solution

    |