The lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent.

If points (1,2,3), (0,-4,3), (2,3,5) and (1,-5,-3) are vertices of tetrahedron, then the point where lines joining the mid-points of opposite edges of concurrent is

If V be the volume of a tetrahedron and V ' be the volume of another tetrahedran formed by the centroids of faces of the previous tetrahedron and V=K V^(prime),t h e nK is equal to a. 9 b. 12 c. 27 d. 81

Prove that the line joining the orthocentre to the centroid of a triangle formed by the focal chord of a parabola and tangents drawn at its extremities is parallel to the axis of the parabola.

A B C D is a tetrahedron and O is any point. If the lines joining O to the vrticfes meet the opposite faces at P ,Q ,Ra n dS , prove that (O P)/(A P)+(O Q)/(B Q)+(O R)/(C R)+(O S)/(D S)=1.

Prove by vector method that the perpendiculars (altitudes) from the vertices to the sides of a triangle are concurrent.

Find the position vector of the centroid of a triangle when the position vectors of the vertices are given.

In each of the following vertices of a triangles are given. Find the coordinates of centroid of each triangle. (4, 7), (8, 4), (7, 11)

In each of the following vertices of a triangles are given. Find the coordinates of centroid of each triangle. (3, -5), (4, 3), (11, - 4)

In each of the following vertices of a triangles are given. Find the coordinates of centroid of each triangle. (-7, 6), (2, -2), (8, 5)