Find ?_C F · dr where C is a circle of radius 2 in the plane x + y + z = 2, centered at (3, 1, -2) and oriented clockwise when viewed from the origin, if F = 2yi - 3xj + (y - x)k ?_C F · dr =
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Since the circle is in the plane x + y + z = 2, we can write z = 2 - x - y. The center of the circle is at (3,1,-2) and the radius is 2. We can parameterize the circle as follows: r(t) = (3 + 2cos(t))i + (1 + 2sin(t))j + (2 - (3 + 2cos(t)) - (1 + 2sin(t)))k Show more…
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