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

9

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

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