EXERCISE 6.1

EXERCISE . . Prove by vector method that if a line is drawn from the centre of a circle to the midpoint of a chord, then the line is perpendicular to the chord. . Prove by vector method that the median to the base of an isosceles triangle is perpendicular to the base. . Prove by vector method that an angle in a semi-circle is a right angle. . Prove by vector method that the diagonals of a rhombus bisect each other at right angles. . Using vector method, prove that if the diagonals of a parallelogram are equal, then it is a rectangle. . Prove by vector method that the area of the quadrilateral ABCD having diagonals AC and BD is | AC BD . Prove by vector method that the parallelograms on the same base and between the same parallels are equal in area. . If G is the centroid of a ABC ∆ , prove that (area of GAB ∆ = (area of GBC ∆ = (area of GCA ∆ (area of ABC D . Using vector method, prove that cos( β β β . Prove by vector method that sin( β β β . A particle acted on by constant forces is displaced from the point ( , , ) to the point ( , , ) . Find the total work done by the forces. . Forces of magnitudes and units acting in the directions , respectively, act on a particle which is displaced from the point with position vector to the point with position vector .Find the work done by the forces. . Find the magnitude and direction cosines of the torque of a force represented by about the point with position vector acting through a point whose position vector is . Find the torque of the resultant of the three forces represented by and ˆ acting at the point with position vector , about the point with position vector