(5 points) Let S be the cube with side length 2, faces parallel to the coordinate...

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(5 points) Let S be the cube with side length 2, faces parallel to the coordinate planes, and centered at the origin, with outward orientation. (a) Calculate the total flux of the constant vector field F = 5 i+ j- 2 k across S by computing the flux through each face separately. flux through the face at x = 1; flux through the face at y = 1; flux through the face at z = 1; flux through the face at x = -1: flux through the face at y = -1: flux through the face at z = -1; Thus the total flux is flux = Calculate the flux across S for any constant vector field F = ai + bj + ck. flux = (Be sure that you can explain why your answers to parts (a) and (b) make sense.) (5 points) Let S be the cube with side length 2, faces parallel to the coordinate planes, and centered at the origin, with outward orientation. (a) Calculate the total flux of the constant vector field F = 5 i+ j- 2 k across S by computing the flux through each face separately. flux through the face at x = 1; flux through the face at y = 1; flux through the face at z = 1; flux through the face at x = -1: flux through the face at y = -1: flux through the face at z = -1; Thus the total flux is flux = Calculate the flux across S for any constant vector field F = ai + bj + ck. flux = (Be sure that you can explain why your answers to parts (a) and (b) make sense.)

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