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 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