Prove analytically : The perpendicular bisector of the sides of a triangle are concurrent.

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

Prove analytically : The altitudes of a triangle are concurrent.

Prove analytically : The line segment joining the midpoints of two sides of a triangle is parallel to the third and half of its length.

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

Find the length of perpendiculars drawn from the origin on the side of the triangle whose vertices are A(2,1),B(3,2) and C(-1,-1).

A test charge q_(0) is brought from infinity along the perpendicular bisector of an electric dipole. The work done on q_(0) by the electric field of the dipole is

Prove analytically : An angle in a semicircle is a right angle.