Home
Class 12
MATHS
If the lines L1: x-2 y+4 z=0,2 x+y+z-4=0...

If the lines `L_1: x-2 y+4 z=0,2 x+y+z-4=0` and `L_2: (x-2)/2=y/1=(z-1)/2 a` are perpendicular, then `a` is equal to

Text Solution

Verified by Experts

The correct Answer is:
0.5
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|9 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE|Exercise JEE Previous Year|26 Videos

Similar Questions

Explore conceptually related problems

If the lines 6x-2 = 3y +1 = 2z-2 and (x-2)/l = (2y-5)/-3 , z=-2 are mutually perpendicular, then: l=

Lines (x-1)/1 = (y-1)/2 = (z-3)/0 and (x-2)/0 = (y-3)/0 = (z-4)/1 are

Statement 1: The lines (x-1)/1=y/(-1)=(z+1)/1 and (x-2)/2=(y+1)/2=z/3 are coplanar and the equation of the plnae containing them is 5x+2y-3z-8=0 Statement 2: The line (x-2)/1=(y+1)/2=z/3 is perpendicular to the plane 3x+5y+9z-8=0 and parallel to the plane x+y-z=0

The lines xy+z=1,3x-y-z+1=0,x+4yz=1 and x+2y+z+1=0 are

Show that the lines x=-y =2z " and " x+2 =2y -1 =-z +1 are perpendicular to each other .

Show that the lines : (i) (x -5)/(7) = (y + 2)/(-5) = (z)/(1) " " and (x)/(1) = (y)/(2) = (z)/(3) (ii) (x - 3)/(2) = (y + 1)/(-3) = (z - 2)/(4) and (x + 2)/(2) = (y - 4)/(4) = (z + 5)/(2) are perpendicular to each other .

Find the equation of the plane passing through the intersection of the planes 2x-3y+z-4=0 and x-y+z+1=0 and perpendicular to the plane x+2y-3z+6=0

CENGAGE-THREE DIMENSIONAL GEOMETRY-Question Bank
  1. Let the line L1: (x-1)/2=(y-2)/3=(z-3)/4 and L2:( x-2)/1= (y-3)/2=(z-k...

    Text Solution

    |

  2. Consider two lines L1: (x-7)/3=(y-7)/2=(z-3)/1 and L2: (x-1)/2=(y+1)/4...

    Text Solution

    |

  3. If the lines L1: x-2 y+4 z=0,2 x+y+z-4=0 and L2: (x-2)/2=y/1=(z-1)/2 a...

    Text Solution

    |

  4. Line drawn perpendicular to plane x+2 y-3 z=21 at point A meets plane ...

    Text Solution

    |

  5. The equation of the plane which has the property that the point Q(5,4,...

    Text Solution

    |

  6. Consider a plane Pi: vec r (2 hati+hatj-hatk)=5, a line L1: ve cr =3 h...

    Text Solution

    |

  7. If L: x-2/a=y-0/b=z-p/c where a, b in I is a line parallel to the line...

    Text Solution

    |

  8. If the angle between the plane x-3 y+2 z=1 and the line x-1/2=y-1/1=z-...

    Text Solution

    |

  9. Aplane P is perpendicular to the vector A=2 i+3 j+6 k and contains the...

    Text Solution

    |

  10. The intersection of the planes 2 x-y-3 z=8 and x+2 y-4 z=14 is the lin...

    Text Solution

    |

  11. Let Q be the foot of perpendicular from the origin to the plane 4 x-3 ...

    Text Solution

    |

  12. If a line passing through A(1,2,3) and B(-1,3,5) meets the plane x+3 y...

    Text Solution

    |

  13. If direction ratios of the normal of the plane which contains the line...

    Text Solution

    |

  14. The point of intersection of the plane vecr .(2 hati-hatj+3 hatk)=6 wi...

    Text Solution

    |

  15. Shortest distance between barz -axis and the line x+y+2 z- 3=0=2 x+3 y...

    Text Solution

    |

  16. If the plane 2 x .+y+2 z harpoons 9 intersects the co-ordinate axes in...

    Text Solution

    |

  17. If the plane 2 x-2 y-z-11=0 makes an angle sin ^-1(lambda) with x -axi...

    Text Solution

    |

  18. The vector barA B=3 hati+4 hatk and overarrowA C=5 hati-2 hatj+4 hatk ...

    Text Solution

    |

  19. The distance of the point (-1,-5,-10) from the point of intersection o...

    Text Solution

    |

  20. Consider two lines in space as L1: vecr1=hatj+2 hatk+lambda(3 hati-hat...

    Text Solution

    |