Home
Class 12
MATHS
Prove that the plane ax + by + cz + d = ...

Prove that the plane ax + by + cz + d = 0 divides the line-segment joining the points `(x_(1),y_(1),z_(1))` and `(x_(2),y_(2),z_(2))` in the ratio `- (ax _(1)+by_(1)+ cz_(1) + d)/(ax_(2) + by_(2) + cz_(2) + d )`

Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO THREE-DIMENSIONAL COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams ( A M . C . Q)|5 Videos

  • INTRODUCTION TO THREE-DIMENSIONAL COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (B Integer Answer Type)|5 Videos

  • INTRODUCTION TO THREE-DIMENSIONAL COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise Very Short Answer Type Questions|60 Videos

  • INTEGRATION BY PARTS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

  • LAWS OF INDICES

    CHHAYA PUBLICATION|Exercise Long Answer Type Questions|6 Videos

Similar Questions

Explore conceptually related problems

Show that the plane ax + by + cz + d = 0 divides, the line segment joining the points (x_1, y_1, z_1) and (x_2, y_2, z_2) in the- ratio -(ax_1+by_1+cz_1+d)/(ax_2+by_2+cz_2+d) .

Show that the plane ax+by+ca+d=0 divides the line joining the points (x_1,y_1,z_1) & (x_2,y_2,z_2) in the ratio - (ax_1+by_1+cz_1+d_1)/(ax_2+by_2+cz_2+d_2)

Find the scalar components and magnitude of the vector joining the points P(x_(1),y_(1),z_(1))andQ(x_(2),y_(2),z_(2)) .

Find the ratio in which the plane 2x+3y+5z=1 divides the line segment joining the points (1,0,-3)and (1,-5,7).

The points P divides the line - segment joining the points A(x_(1),y_(1))andB(x_(2),y_(2)) in the ratio m : n . If P lies on the line ax+by +c=0 , prove that, (m)/(n)=-(ax_(1)+by_(1)+c)/(ax_(2)+by_(2)+c) .

Find the ratio in which the plane 2x + 2y - 2z = 1 divides the line segment joining the points A(2,1, 5) and B(3, 4, 3). Find the co¬ ordinate of point of contact.

The coordinates of any point on the line-segment joining the points ( x _(1) ,y_(1) , z_(1)) and (x_(2), y_(2),z_(2)) are ((x_(1)+kx_(2))/(k + 1),(y _(1) + ky_(2))/(k + 1),(z_(1)+kz_(2))/(k + 1)) , then the value of k will be _

The line segment joining the points (1,2) and (-2, 1) is divided by the line 3x+4y=7 in the ratio

If the lines x=a_(1)y+b_(1),z=c_(1)y+d_(1) and x=a_(2)y+b_(2),z=c_(2)y+d_(2) are perpendicular, prove that, 1+a_(1)a_(2)+c_(1)c_(2)=0 .

the line joining the points (1,1,2) and (3,-2,1) meets the plane 3x+2y+z=6 is __

CHHAYA PUBLICATION-INTRODUCTION TO THREE-DIMENSIONAL COORDINATE GEOMETRY -Short Answer Type Questions
  1. Find the ratio in which the line segment joining A ( 2 , 4 , 5) and B ...

    Text Solution

    |

  2. Let A ( 2 , - 4 , - 3) and B ( - 4 , 2 , 3) be two given points if...

    Text Solution

    |

  3. Find the coordinates of the point in zx-plane which is equidistant fro...

    Text Solution

    |

  4. Find the coordinates of the points on z-axis which are at a distance s...

    Text Solution

    |

  5. A ( 1 , 3 , 0) , B ( 2 , 2 , 1) and C ( 5 , - 1 , 4) are the vertices ...

    Text Solution

    |

  6. IF the z-coordinates of a point C on the line - segment joining the ...

    Text Solution

    |

  7. If A ( 1 , y , z) lies on the line through the points b ( 3 , 2 , - 1...

    Text Solution

    |

  8. Find the coordinates of the centriod of the triangle whose vertices ...

    Text Solution

    |

  9. Using section formula, show that the points A (3 , 2 , -4) , b ( 5 , ...

    Text Solution

    |

  10. The line-segment joining the points A (1 , 2 , 3) and b ( - 3 , 4 ...

    Text Solution

    |

  11. Prove that the xy-plane divides the line-segment joining the points A(...

    Text Solution

    |

  12. If ( - 4 , 7 , 5) , ( 2 , - 6 , - 3) and ( 8 , 2 , - 5) are the co...

    Text Solution

    |

  13. Find the consine of the angle B of the triangle formed by joining t...

    Text Solution

    |

  14. If the point C( x , y , -14) lies on the line-segment overline(AB) ...

    Text Solution

    |

  15. Prove that the plane ax + by + cz + d = 0 divides the line-segment joi...

    Text Solution

    |

  16. The coordinates of the centroid of the triangle ABC are ( 1 , 1, 1) , ...

    Text Solution

    |

  17. The coordinates of the vertex A of the triangle ABC are ( - 3 , -4, ...

    Text Solution

    |

  18. Using section formula show tht the points A ( 9 , 8 , -10) , B ( 3 , 2...

    Text Solution

    |

  19. The coordinates of the centroid of the triangle formed by joining the ...

    Text Solution

    |

  20. Prove that the plane ax - by + cz + d = 0 divides the line-segment jo...

    Text Solution

    |