Home
Class 12
MATHS
The intersection of the spheres x^2+y...

The intersection of the spheres `x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2=z^2-3x+3y+4z=8` is the same as the intersection of one of the spheres and the plane a. `x-y-z=1` b. `x-2y-z=1` c. `x-y-2z=1` d. `2x-y-z=1`

A

`x-y-z=1`

B

`x-2y-z=1`

C

`x-y-2z=1`

D

`2x-y-z=1`

Text Solution

Verified by Experts

The correct Answer is:
d
The given spheres are
`x^(2)+y^(2)+7x-2y-z-13=0" "(i)`
and `x^(2)+y^(2)+z^(2)-3x+3y+2-8=0" "(ii)`
Subtracting (ii) from (i), we get
`10x-5y-5z-5=0`
or `2x-y-z=1`
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 SUBJECTIVE TYPE|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|4 Videos

Similar Questions

Explore conceptually related problems

Find the acute angle between the planes 2x-3y+5z=1 and x-y-z=7 .

Find the plane of the intersection of x^2+y^2+z^2+2x+2y+2=0a n d 4x^2+4y^2+4z^2+4x+4y+4z-1=0.

The plane which passes through the point (3,2,0) and the line (x-3)/1=(y-6)/5=(z-4)/4 is a. x-y+z=1 b. x+y+z=5 c. x+2y-z=1 d. 2x-y+z=5

The projection of the line (x+1)/(-1)=y/2=(z-1)/3 on the plane x-2y+z=6 is the line of intersection of this plane with the plane a. 2x+y+2=0 b. 3x+y-z=2 c. 2x-3y+8z=3 d. none of these

Image of sphere x^(2)+y^(2)+z^(2)=9 in plane 2x+3y+4z-29=0 is

Equation of line of projection of the line 3x-y+2z-1=0=x+2y-z=2 on the plane 3x+2y+z=0 is

Show that the plane 2x-2y+z+12=0 touches the sphere x^2+y^2+z^2-2x-4y+2z-3=0.

CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
  1. The length of the perpendicular drawn from (1,2,3) to the line (x-6...

    Text Solution

    |

  2. If the angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the pl...

    Text Solution

    |

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

    Text Solution

    |

  4. If a plane cuts off intercepts OA = a, OB = b, OC = c from the coordi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), ...

    Text Solution

    |

  8. The radius of the circle in which the sphere x^(I2)+y^2+z^2+2z-2y-4...

    Text Solution

    |

  9. The lines (x-2)/1=(y-3)/2=(z-4)/(-k)a n d=(x-1)/k=(y-4)/2=(z-5)/1 are ...

    Text Solution

    |

  10. The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1a ...

    Text Solution

    |

  11. Two systems of rectangular axes have the same origin. If a plane cu...

    Text Solution

    |

  12. Find the equation of a plane which passes through the point (3, 2, 0...

    Text Solution

    |

  13. The direction ratios of a normal to the plane through (1,0,0)a n d(...

    Text Solution

    |

  14. The centre of the circle given by vecr.(hati+2hatj+2hatk)=15and|vecr-(...

    Text Solution

    |

  15. The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c ...

    Text Solution

    |

  16. Distance of the point P(vecc) from the line vecr=veca+lamdavecb is

    Text Solution

    |

  17. From the point P(a ,b ,c), let perpendicualars P La n dP M be drawn to...

    Text Solution

    |

  18. The plane vecr cdot vecn = q will cotain the line vecr = veca + lambda...

    Text Solution

    |

  19. The projection of point P(vecp) on the plane vecr.vecn=q is (vecs), th...

    Text Solution

    |

  20. The angle between hati and line of the intersection of the plane vecr...

    Text Solution

    |