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

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

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 GEOMETRY

    DISHA PUBLICATION|Exercise Exercise -1 : Concept Builder (Topicwise)|60 Videos

  • STRAIGHT LINES AND PAIR OF STRAIGHT LINES

    DISHA PUBLICATION|Exercise EXERCISE 2: CONCEPT APPLICATOR|30 Videos

  • TRIGONOMETRIC FUNCTIONS

    DISHA PUBLICATION|Exercise EXERCISE-2|30 Videos

Similar Questions

Explore conceptually related problems

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 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)

If cotA+cotB+cotC = k(1/x^2+1/y^2+1/z^2) then the value of k is (A) R^2 (B) 2R (C) /_\ (D) a^2+b^2+c^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))

(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 sphere of constant radius k ,passes through the origin and meets the axes at A,B and C. Prove that the centroid of triangle ABC lies on the sphere 9(x^(2)+y^(2)+z^(2))=4k^(2)

If the plane (x)/(2)+(y)/(3)+(z)/(4)=1 cuts the coordinate axes in A,B,C, then the area of triangle ABC is

A plane meets the coordinate axes at P, Q and R such that the centroid of the triangle is (3,3,3). The equation of he plane is (A) x+y+z=9 (B) x+y+z=1 (C) x+y+z=3 (D) 3x+3y+3z=1

DISHA PUBLICATION-THREE DIMENSIONAL GEOMETRY -Exercise -2 : Concept Applicator
  1. The line which contains all points (x, y, z) which are of the form (x,...

    Text Solution

    |

  2. Show that the points A(1,2,3), B(-1,-2,-1), C(2,3,2), D(4,7,6) are the...

    Text Solution

    |

  3. The shortest distance between the line 1+x=2y=-12z and x=y+2=6z-6 is

    Text Solution

    |

  4. The line which passes through the origin and intersect the two lines (...

    Text Solution

    |

  5. The angle between the lines (x+1)/2 = (y+3)/2 = (z-4)/-1 and (x-4)/1 =...

    Text Solution

    |

  6. The distance between the line given by vecr= hati+hatj + lamda(hati-2...

    Text Solution

    |

  7. Find the point on the line (x+2)/3=(y+1)/2=(z-3)/2 at a distance of 3s...

    Text Solution

    |

  8. The coordinates o the foot of the perpendicular drawn from the orig...

    Text Solution

    |

  9. If A,B,C are point (1,0,4) , (0,-1,5) and (2,-3,1) respectively , then...

    Text Solution

    |

  10. If from a point P(a ,b ,c) prpendiculars P Aa n dP B are drawn to y za...

    Text Solution

    |

  11. The equation of the plane which makes with coordinate axes a triangle ...

    Text Solution

    |

  12. The plane ax+by=0 is rotated through an angle alpha about its line of ...

    Text Solution

    |

  13. The plane x + 3y + 13 = 0 passes through the line of intersection of t...

    Text Solution

    |

  14. A variable plane at distance of 1 unit from the origin cuts the coordi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. If the distance between the plane Ax 2y + z = d and the plane contain...

    Text Solution

    |

  18. If the angle between the line x=(y-1)/(2)=(z-3)(lambda) and the plane ...

    Text Solution

    |

  19. If two points are P(7, -5, 11) and Q(-2, 8, 13), then the projection o...

    Text Solution

    |

  20. Radius of the circle vec(r(2))+vecr(2hati-2hatj-4hatk)-19=0. vecr.(hat...

    Text Solution

    |