1. 2. 3. The temperature, 0C, at every point is space is given by the scalar function = xye Find the temperature at the point (1,2, 0.5) The Electric Field in space is given by the following vector function: E(x, y, z) = x=i+ zi+y=j + xyk V m (a) Find E at the point (3,2,5). (b) Hence, find the magnitude of the electric field at the point. The flight path of a drone is given by, r(t)t cost it sin tj+tk (a) Find the velocity at time t. (b) Find the distance travelled by the by the drone from t = 0 tot = t- Write down the integral without evaluating it. (c) Evaluate the integral from t = 0 to t = 1 given that, x + a = 1 + In [x + x + a + 1/2 + a] 4. 5. A beam of light passes through the hole located at the coordinates (2, 3, 6) in the direction -i + 2 - 4k. Determine the following: (i) The equation of the line describing the beam. (!!) The location where the beam hits the x-y plane. A wireless activated toy car moves on a flat surface in a closed path given by x = A cos wt, and y = B sin wt, B > A. (i) Find the shape of the closed path by relating x to y through elimination of the functions sin wt and cos wt using the trigonometric relation sin wt + coswt = 1. Find the velocity at time t. Evaluate it at time t = 2. (ii) (iii) Find the acceleration vector at time t. Evaluate it at time t = 2. (iv) Hence, find the radius of curvature, p, at t = 2, given that the centripetal acceleration, a, is given by a = v/p, where v is the speed at the time.