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`

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 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)).

The plane 2x+3y+4z=1 meets the coordinate axis in A, B, C. The centroid of the DeltaABC 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

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

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

The plane x+2y-z=4 cuts the sphere x^2+y^2+z^2-x+z-2=0 in a circle of radius (A) sqrt(2) (B) 2 (C) 1 (D) 3

The line (x-4)/1=(y-2)/1=(z-k)/2 lies exactly on the plane 2x-4y+z=7 then the value of k is (A) 7 (B) -7 (C) 1 (D) none of these