3. Let S be the part of the surface x + y + z = 1...

 

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3. Let S be the part of the surface x² + y² + z² = 1 such that y ≤ 0 and z ≥ 0, oriented with upwards unit normal. Let C be the boundary of S, oriented anti-clockwise when viewed from above. (a) Sketch the surface S, indicating the orientation of S and C. (b) Give a parametrisation for C in terms of a parameter t, with t increasing, beginning and ending at the point (1,0,0). (c) Using your parametrisation in part (b), use MATLAB to plot the curve C. (d) Find the flux of the vector field across S. F(x, y, z)=zj+e x²+y² k 3. Let S be the part of the surface x² + y² + z² = 1 such that y ≤ 0 and z ≥ 0, oriented with upwards unit normal. Let C be the boundary of S, oriented anti-clockwise when viewed from above. (a) Sketch the surface S, indicating the orientation of S and C. (b) Give a parametrisation for C in terms of a parameter t, with t increasing, beginning and ending at the point (1,0,0). (c) Using your parametrisation in part (b), use MATLAB to plot the curve C. (d) Find the flux of the vector field across S. F(x, y, z)=zj+e x²+y² k

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a The surface S is part of the hyperboloid 2 y 22 1 where y 0 an... View the full answer