Find ?_C F?? ? dr?? where C is a circle of radius 2 in the plane x + y + z = 5, centered at (2, 4, -1) and oriented clockwise when viewed from the origin, if F?? = 3yi?? ? 2xj?? + 5(y ? x)k?? ?_C F?? ? dr?? =
Added by Holly F.
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We can do this by using spherical coordinates. Let's denote the center of the circle as P(2,4,-1) and the radius as r = 2. The normal vector to the plane x + y + z = 5 is n = (1,1,1). We can find two orthogonal vectors in the plane by taking the cross product of Show more…
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