[理工] [工數] 98中正機械甲
98中正機械甲組工數第二題 想了好久想不出來 請各位幫幫忙Q_Q
2.Assume that F=zi+xj+yk, where i,j,k are three unit vectors in a
Cartesian coordinate system. C represent the curve of intersection
of the plane x+y+z=0 and the sphere x^2 + y^2 + z^2=1.
(a) Determine the surface area enclosed by the curve C.
(b) Assume that the surface area enclosed by c is oriented upward.
Determine the unit vector normal to the area enclosed by C.
(c) Determine the lntegral along the curve C;∮F‧dr
c
Hint: 1. The area of an ellipse (x^2 / a^2) + (y^2 / b^2) =1 is πab.
2. Stokes' Theorem ∮F‧dr = ∫∫(curlF)‧ndS.
c s
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