Home
Class 12
MATHS
A variable plane at a distance of 1 unit...

A variable plane at a distance of 1 unit from the origin cuts the axes at A, B and C. If the centroid `D(x, y, z)` of `triangleABC` satisfies the relation `(1)/(x^2)+(1)/(y^2)+(1)/(z^2)=K,` then the value of K is

A

`3`

B

`1`

C

`(1)/(3)`

D

`9`

Text Solution

Verified by Experts

The correct Answer is:
(d)
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|28 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|14 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise For Session 4|7 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

A variable plane at distance of 1 unit from the origin cuts the coordinte axes at A,B and C. If the centroid D(x,y,z) of triangle ABC satisfies the relation 1/x^2+1/y^2+1/z^2=k then the value of k is (A) 3 (B) 1 (C) 1/3 (D) 9

A variable plane (x)/(a)+(y)/(b)+(z)/(c)=1 at a unit distance from origin cuts the coordinate axes at A,B and C. Centroid (x,y,z) satisfies the equation (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=K. The value of K is (A) 9 (B) 3(C) (1)/(9)(D)(1)/(3)

(i) A variable plane, which remains at a constant distance '3p' from the origin cuts the co-ordinate axes at A, B, C. Show that the locus of the centroid of the triangle ABC is : (1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (1)/(p^(2)) . (ii) A variable is at a constant distance 'p' from the origin and meets the axes in A, B, C respectively, then show that locus of the centroid of th triangle ABC is : (1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (9)/(p^(2)).

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A,B,C. Show that the locus of the centroid of triangle ABC is (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(p^(2))

The plane 2x+3y+4z=12 meets the coordinate axes in A,B and C. The centroid of triangleABC is

A variable plane which remains at a constant distance p from the origin cuts coordinate axes in A,B,C.sof centroid of tetrahedron OABC is y^(2)z^(2)+z^(2)x^(2)+x^(2)y^(2)=kx^(2)y^(2)z^(2) where k is equal to

A variable plane cutting coordinate axes in A, B, C is at a constant distance from the origin. Then the locus of centroid of the triangleABC is

ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. The orthogonal projection A' of the point A with position vector (1, 2...

    Text Solution

    |

  2. The equation of the line passing through (1, 1, 1) and perpendicular t...

    Text Solution

    |

  3. A variable plane at a distance of 1 unit from the origin cuts the axes...

    Text Solution

    |

  4. The angle between the lines AB and CD, where A(0, 0, 0), B(1, 1, 1), C...

    Text Solution

    |

  5. The shortest distance of a point (1, 2, -3) from a plane making interc...

    Text Solution

    |

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

    Text Solution

    |

  7. The direction ratios of the line I1 passing through P(1, 3, 4) and per...

    Text Solution

    |

  8. Equation of the plane through three points A, B and C with position ve...

    Text Solution

    |

  9. OABC is a tetrahedron. The position vectors of A, B and C are I, i+j a...

    Text Solution

    |

  10. The plane x-y-z=4 is rotated through an angle 90^(@) about its line of...

    Text Solution

    |

  11. A(xy),(yz),A(zx) be the area of projections oif asn area a o the xy,yz...

    Text Solution

    |

  12. Through a point P(h,k,l) a plane is drawn at righat angle to OP to mee...

    Text Solution

    |

  13. The volume of the tetrahedron included between the plane 3x+4y-5z-60=0...

    Text Solution

    |

  14. The angle between the lines whose direction cosines are given by the ...

    Text Solution

    |

  15. The distance between the line r=2hat(i)-2hat(j)+3hat(k)+lambda(hat(i)-...

    Text Solution

    |

  16. The cartesian equations of the plane perpendicular to the line (x-1)/(...

    Text Solution

    |

  17. Let P(3,2,6) be a point in space and Q be a point on line vec r=( hat...

    Text Solution

    |

  18. A plane makes interceptsOA, OB and OC whose measurements are a, b and ...

    Text Solution

    |

  19. The radius of the circle in which the sphere x^2+y^2+z^2+2x-2y-4z-19=0...

    Text Solution

    |

  20. Let veca=hati+ hatj and vecb = 2hati-hatk . The point of intersection ...

    Text Solution

    |