Answer Happy

= (i) Given vectors a = ê + + and b = 2î – - , where î, ŷ, and î are the usual Cartesian unit vectors, find (a) the angle between the vectors a and b; (b) b-a; (c) a unit vector in the direction of vector c = b - a; (d) the volume of the parallelepiped a . - (0 X c); (e) the area of the parallelogram determined by the vectors a and b. (ii) The position vector of a particle, where w,a and b are constants, is given by х r = a cos wt + b sin wt. (a) Show that the equation of motion is der + war = 0; dt2 = (b) Also show that dr rx dt = wa x b. (iii) If the acceleration vector a(t) has constant magnitude but changes direction with t, and a(t) + 0, show that a and da/dt are perpendicular vectors.