Show that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.

Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.

The sum of the three vectors determined by the medians of triangle directed from the vertices is

Point where three medians of a triangle meet.

The sum of these three vectors is :

Three coinitial vectors of magnitudes a, 2a and 3a meet at a point and their directions are along the diagonals if three adjacent faces if a cube. Determined their resultant R. Also prove that the sum of the three vectors determinate by the diagonals of three adjacent faces of a cube passing through the same corner, the vectors being directed from the corner, is twice the vector determined by the diagonal of the cube.

Prove that the sum of the vectors directed from the vertices to the mid-points of opposite sides of a triangle is zero.

Show that the sum of the three altitudes of a triangle is less than the sum of three sides of the triangle.

The sum of three altitudes of a triangle is