Let ${ \vec { F } } = - 3 x z \vec { i } + 4 ( y - x ) \vec { j } + 4 x \vec { k }$

question 32

Essay

Let ${ \vec { F } } = - 3 x z \vec { i } + 4 ( y - x ) \vec { j } + 4 x \vec { k }$
(a)By direct computation, find the circulation of $\vec { F }$ around the circle of radius a, $\vec { r } ( t ) = \alpha \cos t \vec { i } + \alpha \sin t \vec { j }$ for 0 $\le$ t $\le$ 2 $\pi$ .
(b)Use this result to find the $\vec { k }$ component of $\operatorname { curl } \vec { F } ( 0,0,0 )$

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