Question: (b) A surface S in 3D space is described by the equation r? +y? = 4, and is bounded by the planes 2 =

(b) A surface S in 3D space is described by the equation

(b) A surface S in 3D space is described by the equation r? +y? = 4, and is bounded by the planes 2 = 0, 2 = 2, x = 0, and y = 0. The point D lies on the surface S with Cartesian Co-ordinates r = 2, z = 0. %3D i. Sketch and shade the surface S, and show the point D on your sketch. 2 marks ii. Determine the Spherical Co-ordinates of the point D. Your answer should clearly indicate the axes for the spherical co-ordinate frame. iii. The direction of the base vectors for Spherical Co-ordinate systems vary de- pending on location, but the base vectors for the Cartesian co-ordinate system (i, j, k) have fixed directions. Discuss why this is so, using the point D as an example. 4 marks 5 marks

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