Hello, I really need someone good at math who can solve this problem! Thanks in advance! :
Let C be the ellipse in which the plane 2x + 3y - z = 0 meets the cylinder x^2 + y^2 = 12. Show, without evaluating, either line integral directly, that the circulation of the field F = xi + yj + zk around C in either direction is zero.
2007-04-26 14:54:19 · 4 answers · asked by djibouti1989 1 in Science & Mathematics ➔ Mathematics
Using stokes's theorem, we know that the circulation around the ellipse is the integral of the curl of the vector field over any orientable surface bounded by that ellipse. However, it is readily seen that ∇×F is everywhere 0, so the integral of the curl, and thus the circulation, is also 0.
2007-04-26 15:44:12 · answer #1 · answered by Pascal 7 · 0⤊ 0⤋
Draw a sketch of the plane, cylinder, and infinitesimal vectors summed up in the circulation integral. If you choose the perspective of your sketch correctly, you will either find a symmetry argument or an exact differential that shows that the integral (representing the circulation) is zero.
Good luck.
2007-04-26 15:07:05 · answer #2 · answered by Indicator Veritatis 2 · 0⤊ 0⤋
Send this problem to lilkraut@yahoo.com
2007-04-26 14:58:31 · answer #3 · answered by Anonymous · 0⤊ 0⤋
what type of question is this algebra?
2007-04-26 15:05:41 · answer #4 · answered by mecca laran 4 · 0⤊ 0⤋