| > || a | −−−−− | b || (c) | a −−−−− b | < | a | + | b | (d) | a −−−−− b | > || a | −−−−− | b || When does the equality sign above apply? . Given a + b + c + d = , which of the following statements are correct : (a) a , b , c , and d must each be a null vector, (b) The magnitude of ( a + c ) equals the magnitude of ( b + d ), (c) The magnitude of a can never be greater than the sum of the magnitudes of b , c , and d , (d) b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d , if they are collinear ? .
Three girls skating on a circular ice ground of radius m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in Fig. . . What is the magnitude of the displacement vector for each ?
For which girl is this equal to the actual length of path skate ? . A cyclist starts from the centre O of a circular park of radius km, reaches the edge P of the park, then cycles along the circumference, and returns to the centre along QO as shown in Fig. .
. If the round trip takes min, what is the (a) net displacement, (b) average velocity, and (c) average speed of the cyclist ? Fig. .
. On an open ground, a motorist follows a track that turns to his left by an angle of after every m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.