Prove the following by vector method. Altitudes of a triangle are concurrent.

Prove by vector method that the medians of a triangle are concurrent.

Prove the following by vector method. in any triangle ABC, a = bcosC+c cosB.

Prove the following by vector method. Measure of the angle between two diagonals of a cube is cos^-1 (1/3)

Prove analytically : The altitudes of a triangle are concurrent.

Prove the following by vector method. In a triangle AOB, mangleAOB = 90^@ . If P and Q are the points of trisection of AB, prove that OP^2+OQ^2 = 5/9 AB^2

Prove the following by vector method. The diagonals of a rhombus are at right angles.

Prove the following by vector method. Median to the base of an isosceles triangle is perpendicular to the base.

Prove the following by vector method. The parallelogram whose diagonals are equal is a rectangle.

Prove the following by vector method. An angle inscribed in a semi-circle is a right angle.