Home
Class 12
MATHS
Equation of the plane that contains the ...

Equation of the plane that contains the lines `r=(hat(i)+hat(j))+lambda(hat(i)+2hat(j)-hat(k)) and , r=(hat(i)+hat(j))+mu(-hat(i)+hat(j)-2hat(k))` is

Text Solution

Verified by Experts

The correct Answer is:
` = (5)/(sqrt(3))` unit.
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    OSWAAL PUBLICATION|Exercise Topic - 3 (Short answer type questions - II)|9 Videos

  • SOLVED PAPER ( Topper Answers March - 2015 )

    OSWAAL PUBLICATION|Exercise PART - E|4 Videos

  • VECTOR ALGEBRA

    OSWAAL PUBLICATION|Exercise Topic - 4 (Short Answer Type Questions - II|7 Videos

Similar Questions

Explore conceptually related problems

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

Find the angle between the following pairs of lines : r=3hat(i)+hat(j)-2hat(k)+lambda(hat(i)-hat(j)-2hat(k)) " and " r=2hat(i)-hat(j)-56hat(k)+mu(3hat(i)-5hat(j)-4hat(k)) .

Find the angle between the following pairs of lines : r=2hat(i)-5hat(j)+hat(k)+lambda(3hat(i)+2hat(j)+6hat(k)) " and " r=7hat(i)-6hat(k)+mu(hat(i)+2hat(j)+2hat(k))

Find the angle between the pair of lines r=3hat(i)+2hat(j)-4hat(k)+lambda(hat(i)+2hat(j)+2hat(k)) r=5hat(i)-4hat(k)+mu(3hat(i)+2hat(j)+6hat(k))

Find the angle between the pair of lines vec(r)=3hat(i)+5hat(j)-hat(k)+lambda(hat(i)+hat(j)+hat(k))" and "vec(r)=7hat(i)+4hat(k)+mu(2hat(i)+2hat(j)+2hat(k))

Find the vector and cartesian equations of a plane containing the two lines vec(r) = (2 hat(i) + hat(j) - 3 hat(k)) + lambda(hat(i) + 2 hat(j) + 5 hat(k)) and vec(r) = (3hat(i) + 3 hat(j) + 2 hat(k)) + lambda (3 hat(i) - 2 hat(j) + 5 hat(k)) . Also show that the line vec(r) = (2 hat(i) + 5 hat(j) + 2 hat(k)) + p (3 hat(i) - 2 hat(j) + 5 hat(k)) lies in the plane.

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

Find the angle between the following pairs of lines : vec(r)=3hat(i)+2hat(j)-4hat(k)+lambda(hat(i)+2hat(j)+2hat(k)) " & " vec(r)=5hat(i)-2hat(j)+mu(3hat(i)+2hat(j)+6hat(k)) Note : Angle between two lines is the angle between vec(b_(1)) " and " vec(b_(2))

OSWAAL PUBLICATION-THREE DIMENSIONAL GEOMETRY-Topic - 3 (Long answer type questions - II)
  1. Find the equation of the plane passing through the line of intersecti...

    Text Solution

    |

  2. Find the distance between the point (7,2,4) and the plane determined b...

    Text Solution

    |

  3. Find the distance of the point (-1,-5,-10) from the point of intersect...

    Text Solution

    |

  4. Find the equation of the plane through the line of intersection of the...

    Text Solution

    |

  5. Find the distance of the point (2,12,5) from the point of intersectio...

    Text Solution

    |

  6. Find the equation of the plane that contains the point A(1,-1,2) and ...

    Text Solution

    |

  7. Show that the lines (x+3)/(-3) = (y-1)/1 = (z-5)/5 and (x+1)/ (-1) = (...

    Text Solution

    |

  8. Find the coordinates of the point where the line through (3,-4,-5) and...

    Text Solution

    |

  9. Find the equation of the plane through the line of intersection of the...

    Text Solution

    |

  10. Find the vector equation of the plane passing through three points ...

    Text Solution

    |

  11. Find the equation of the plane determined by the points (A(3,-1,\ 2...

    Text Solution

    |

  12. Find the vector equation of the line passing through the point (1,2...

    Text Solution

    |

  13. Equation of the plane that contains the lines r=(hat(i)+hat(j))+lambd...

    Text Solution

    |

  14. If the lines (x-1)/(-3)=(y-2)/(-2y)=(z-3)/2 and (x-1)/k=(y-2)/1-(z-3)...

    Text Solution

    |

  15. Find the vector and cartesian equations of a plane containing the two ...

    Text Solution

    |

  16. Find the distance of the point (-1,-5,-10) from the point of intersect...

    Text Solution

    |

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

    Text Solution

    |

  18. Find the vector equation of the plane which contains the line of in...

    Text Solution

    |

  19. Find the coordinates of the foot of the perpendicular and the perpendi...

    Text Solution

    |

  20. Find the equation of the plane passing through the point P(1,1,1) and...

    Text Solution

    |