1. The vector function F(x, y,z) is given by F(x. y. z) = (z + y= )i + (2xy + 2)j + (x+ y)k (i) Explain why the vector function F can be written as Vp (x, y. z). (ii) Hence find the scalar function p (x. y. z). (iii) Calculate the line integral. (1,2.1) F . dr (0,0.0) 2. Calculate the line integral J F . dr with the vector function F given by F(x. y.z) = yi- xj +k (i) over the path of the helix given by x = 2 cost ,y = 2 sint ,z = 3t for one loop ie. fort = 0 to t = 2n. over the straight line given by x- 1 y- 2 W| N 5 2 = from point (1.2.0) to point (6.4.3). 3. (i) Sketch the region over which the double integral below is performed ['[" (x + y )dxdy Reverse the order of the integration and hence evaluate the integral. 4. The transformation equations from the x - y to u - v co-ordinate systems are given by 1=xty xty Construct the region in the u - v co-ordinate system corresponding to the triangle ABC in the x - y co-ordinate system. C B 1