1.Convert the following vectors to cylindrical and spherical systems: F = 10,+ya, +za, G = *+y* [ra, + ya, + za:] 2.The acceleration of a particle is given bya = 2.4a,m/s. The initial position of the particle is r = (0, 0, 0), while its initial velocity isu =-2a, + 5a,m/s. (a) Find the position of the particle at time t = 1. (b) Determine the velocity of the particle as a function of t 3.Prove that (1) V (VA) = VV A+ AVV where V is a scalar field and A is a vector field, (2) Evaluate V. (VA) whenA 2ray + 3yay - 4zazand V = ryz. Let A = psinda, + pas. Evaluate f, A dl given that (1) L is contour given fig 1.0 fig 1.0 4.A charge distribution in free space hasp, = 2rnC/m for 0