If a plane meets the coordinate axes at A, B, C such that the centroid of the triangle ABC is the point `(1,r,r^(2))`, then show that the equation of the plane is ` r^(2)x+ry+z=3r^(2)`.

A plane meets the coordinates axes in A, B, C such that the centroid of the triangle ABC is the point (a,a,a) .Then the equation of the plane is x+y+z=p , where p is ___

A plane meets the coordinates axes at L, M, N respectively, such that the centroid of the triangle LMN is (1,-2,3) . Find the equation of the plane.

If a plane meets the equations axes at A ,Ba n dC such that the centroid of the triangle is (1,2,4), then find the equation of the plane.

If a plane meets the equations axes at A ,Ba n dC such that the centroid of the triangle is (1,2,4), then find the equation of the plane.

A plane meets the coordinates axes respectively at A, B and C such that the centroid of the triangle ABC is ( 3, 3, 3) . If the equation of the plane is x+y+z=p. Then p is equal to

A plane meets the coordinate axes at P, Q, R such that the centroid of the triangle PQR ar (a, b, c). If the equation of the plane is (x)/(a)+(y)/(b)+(z)/(c )=m , then the value of m is -

A plane meets the co-ordinate axes at the points A, B, C respectively in such a way that the centroid of Delta ABC is (1, r, r^(2)) for some real r. If the plane passes through the point (5, 5, -12) then r =

In triangle ABC, if r_(1) = 2r_(2) = 3r_(3) , then b : c is equal to

The coordinates of the vertex A of the triangle ABC are (2,5), if the centroid of the triangle is at (-2, 1), then the coordinates of the mid-point of the side BC are-

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) .