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.

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

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 all vectors drawn from the centre of a regular octagon to its vertices is the zero vector.

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

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

Prove using vectors: If two medians of a triangle are equal, then it is isosceles.

Prove that the locus of a point which moves such that the sum of the square of its distances from the vertices of a triangle is constant is a circle having centre at the centroid of the triangle.

Show that the sum of the three altitudes of a triangle is less than the sum of three sides of the triangle. GIVEN :triangle A B C in which A D_|_B C ,B E_|_A C and C F_|_A Bdot PROVE : A D+B E+C F < A B+B C+A C