Consider the surface S with surface parameterisation r(u, v) = 3u sin(v) i + 4u sin(v)j + vk for 0 ≤u≤ 1 and 0 ≤ v ≤ π. Ər ər (1) Calculate the tangent vectors, and to the surface S. du əv' (2) Use your results in part 1 to find a normal vector N to the surface S. (3) Find the length of the normal vector to the surface S. (4) Use the result in part 3 (and the surface parameterisation) to find the surface area of S. Start by writing the general mathematical expression for finding the surface area of a surface.

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