Home
Class 12
MATHS
For what value (s) of a will the two poi...

For what value (s) of `a` will the two points `(1,a,1) and (-3,0,a)` lie on opposite sides of the plane `3x+4y-12z+13=0?`

Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos
  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise ARCHIVES INTEGER TYPE|1 Videos

Similar Questions

Explore conceptually related problems

Find the value of a if the points (1, 2) and (3, 4) are of opposite side of the line 3x - 4y + a = 0

If the points (1,2) and (3, 4) are on the opposite side of the line 3x - 5y + a = 0, then :

Do the points (-2,5),(3,-4) lie on the same or opposite sides of the circle 3x^2+3y^2-5x-93=0 ?

The range of values of theta in the interval (0, pi) such that the points (3,5) and (sin theta , cos theta) lie on the same side of the line x+y-1=0 , is

Show that the equation of the plane which passes through the point (1,2,3) and parallel to the plane 3x+4y-5z=0 is 3x+4y-5z+4=0 .

Find the equation of the plane which passes through the point (2,1,-1) and is orthogonal to each of the planes x-y+z=1 and 3x+4y-2z=0 .

Show that the equation of the plane passing through the point (1,2,3) and parallel to the plane. 3x + 4y - 5z = 3 is given by 3x + 4y - 5z = -4.

Find the equation of a plane which passes through the point (1, 2, 3) and which is equally inclined to the planes x-2y+2z-3=0 and 8x-4y+z-7=0 .

Prove that the equation of the plane which passes through the point (-1,3,2) and is prependicular to the planes x+2y+2z=5 and 3x+3y+2z=8 is 2x-4y+3z+8=0 .

Show that the equation of the plane passing through the point (1,2,3) and parallel to the plane 3x+4y-5z=3 is given by 3x+4y-5z=-4 .

CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
  1. A variable plane passes through a fixed point (alpha,beta,gamma) an...

    Text Solution

    |

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

    Text Solution

    |

  3. The perpendicular distance of a corner of unit cube from a diagonal no...

    Text Solution

    |

  4. If the direction cosines of a variable line in two adjacent points be ...

    Text Solution

    |

  5. the image of the point (-1,3,4) in the plane x-2y=0 a.(-(17)/(3),(19)/...

    Text Solution

    |

  6. The ratio in which the plane vec rdot (vec i-2 vec j+3 vec k )=17 d...

    Text Solution

    |

  7. Column I, Column II A tx=1,f(x)={logx ,x<1 2x-x^2, xgeq1 , p. is ...

    Text Solution

    |

  8. The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambd...

    Text Solution

    |

  9. If angle theta bertween the line (x+1)/1=(y-1)/2=(z-2)/2 and the plane...

    Text Solution

    |

  10. The length of the perpendicular drawn from (1,2,3) to the line (x-6...

    Text Solution

    |

  11. A plane makes intercepts O A ,O Ba n dO C whose measurements are a,b a...

    Text Solution

    |

  12. The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2+z...

    Text Solution

    |

  13. The shortest distance from the plane 12 x+4y+3z=327 to the sphere ...

    Text Solution

    |

  14. A line makes an angel theta with each of the x-and z-axes. If the ...

    Text Solution

    |

  15. Find the equation of a straight line in the plane vec r* vec n=d ...

    Text Solution

    |

  16. What is the nature of the intersection of the set of planes x+a y+(b...

    Text Solution

    |

  17. Let P1 denote the equation of a plane to which the vector ( hat i+ h...

    Text Solution

    |

  18. Let P M be the perpendicular from the point P(1,2,3) to the x-y pla...

    Text Solution

    |

  19. If the plane x/2+y/3+z/6=1 cuts the axes of coordinates at points, A ,...

    Text Solution

    |

  20. For what value (s) of a will the two points (1,a,1) and (-3,0,a) lie ...

    Text Solution

    |