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

For what value (s) of a will the two points `(1,a ,1)a n d(-3,0,a)` lie on opposite sides of the plane `3x+4y-12 z+13=0?` a. `a >-1ora >1//3` b. `a=0` only c. `0

A

`alt-1oragt1//3`

B

a=0 only

C

`0ltalt1`

D

`-1ltalt1`

Text Solution

Verified by Experts

The correct Answer is:
a
We must have `(3+ 4a -12+13)(-9-12a+13) lt 0`.
or `" "(a+1)(12a-4) gt 0`
or `" " a lt -1 or a gt 1//3`
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Exercise (Reasoning Questions)|10 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Exercise (Subjective)|16 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|34 Videos

Similar Questions

Explore conceptually related problems

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?

For a 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-12x+13-0?

Are the points (2,1) and (-3,5) on the same or opposite side of the line 3x - 2y + 1 = 0 ?

Show that the points (1, 1, 1) and (-3, 0, 1) are equidistant from the plane 3x+4y-12 z+13=0.

Prove that the point (2, -1) and (1, 1) are on the opposite sides of the straight line 3x+4y-6=0 .

Show that the points (-3,0,1) and (1,1,1) are equidistant from the plane 3x+4y-12z+13=0 .

Show that the points (1,-1,3) and (3, 4, 3) are equidistant from the plane 5x +2y + -7z + 8 = 0.

CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
  1. The three planes 4y+6z=5,2x+3y+5z=5a n d6x+5y+9z=10 a. meet in a poi...

    Text Solution

    |

  2. The equation of the plane through the line of intersection of the plan...

    Text Solution

    |

  3. Equation of the pane passing through the points (2,2,1)a n d(9,3,6)...

    Text Solution

    |

  4. Value of lamda such that the line (x-1)/(2)=(y-1)/(3)=(z-1)/(lamda) is...

    Text Solution

    |

  5. The equation of the plane passing through the intersection of x + 2y +...

    Text Solution

    |

  6. The plane 4x+7y+4z+81=0 is rotated through a right angle about its ...

    Text Solution

    |

  7. The vector equation of the plane passing through the origin and the li...

    Text Solution

    |

  8. The two lines vecr=veca+veclamda(vecbxxvecc) and vecr=vecb+mu(veccxxve...

    Text Solution

    |

  9. The projection of the line (x+1)/(-1)=y/2=(z-1)/3 on the plane x-2y+z=...

    Text Solution

    |

  10. The direction cosines of a line satisfy the relations lambda(l+m)=n ...

    Text Solution

    |

  11. The intercepts made on the axes by the plane the which bisects the ...

    Text Solution

    |

  12. Find the angle between the lines whose direction cosines are given by ...

    Text Solution

    |

  13. A sphere of constant radius 2k passes through the origin and meets ...

    Text Solution

    |

  14. A plane passes through a fixed point (a ,b ,c)dot The locus of the ...

    Text Solution

    |

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

    Text Solution

    |

  16. Find the equation of a straight line in the plane vecr.vecn=d which is...

    Text Solution

    |

  17. What is the equation of the plane which passes through the z-axis and ...

    Text Solution

    |

  18. A straight line L on the xy-plane bisects the angle between O Xa n dO ...

    Text Solution

    |

  19. For what value (s) of a will the two points (1,a ,1)a n d(-3,0,a) l...

    Text Solution

    |

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

    Text Solution

    |