Home
Class 12
MATHS
Prove that the lines x=ay +b,z =cy +d...

Prove that the lines x=ay +b,z =cy +d and x=a'y +b' z =c'y +a'
are perpendicular if aa'+cc' +1=0

Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHECK YOUR UNDERSTANDING|10 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise COMPETITION FILE|25 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 11|10 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (1)|12 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise CHAPTER TEST 10|12 Videos

Similar Questions

Explore conceptually related problems

If the lines x=ay +b, z=cy+d and x=a'y + b', z=c'y + d' are perpendicular, then

If lines x=ay+b, z= cy +d " and " x=a' z+b y+c' z+ d' are perpendicular then

Fid the condition if lines x=ay+b,z=cy+d and x=a'y+b',z=c'y+d are perpendicular.

The two lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d' are perpendicular to each other, if

The two lines x=ay+b,z=cy+d and x=a'y+b',z=c'y+d' will be perpendicularm if and only if

The dr's of the line x=ay+b,z=cy+d are

Under which one of the following conditions are the lines x= ay + b ; z = cy + d and x = ey +f ; z = gy + h perpendicular

the two lines x=ay+b,z=cy+d and x=a\'y+b,z=c\'y+d\' will be perpendicular, if and only if: (A) aa\'+cc\'=1=0 (B) aa\'+bb\'+cc\'=1=0 (C) aa\'+bb\'+cc\'=0 (D) (a+a\')+(b+b\')+(c+c\')=0

MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY -REVISION EXERCISE
  1. If the direction cosines of a variable line in two adjacent points be ...

    Text Solution

    |

  2. Prove that the straight lines whose direction cosines are given by the...

    Text Solution

    |

  3. Prove that the line joining the mid-points of the two sides of a tr...

    Text Solution

    |

  4. Find the vector equation of the line passing through (1, 2, 3) and ...

    Text Solution

    |

  5. Prove that the lines x=ay +b,z =cy +d and x=a'y +b' z =c'y +a' ...

    Text Solution

    |

  6. Prove that the line joining the points vec(6a) - vec(4b) + vec(4c) and...

    Text Solution

    |

  7. Find the vector equation o the line passing through (1,2,3) and parall...

    Text Solution

    |

  8. Find the vector equation of the line passing through the point (1,"...

    Text Solution

    |

  9. find the coordinates of point where the line through (3,-4,-5) and (2,...

    Text Solution

    |

  10. Show that equation of the plane passing through a point having positio...

    Text Solution

    |

  11. Find the distance of the point (2,3,4) from the plane 3x+2y+2z+5=0 mea...

    Text Solution

    |

  12. Find the distance of the point with position vector - hati - 5 hatj - ...

    Text Solution

    |

  13. Find the point R, Where the line joining P (1,3,4) and Q (-3,5,2) cuts...

    Text Solution

    |

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

    Text Solution

    |

  15. If from a point P(a ,b ,c) perpendiculars P Aa n dP B are drawn to Y Z...

    Text Solution

    |

  16. If O be the origin and the coordinates of P be(1," "2," "" "3) , th...

    Text Solution

    |

  17. Find the equation of the plane , which contains the line of intersecti...

    Text Solution

    |

  18. Prove that the shortest distance between the diagonals of a rectangula...

    Text Solution

    |

  19. A variable plane is at a constant distance p from the origin and meets...

    Text Solution

    |