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 $\operatorname { curl } \vec { F } ( 0,0,0 )$

Question

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 $\operatorname { curl } \vec { F } ( 0,0,0 )$

Quizplus · Accepted Answer

The Answer of 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 $\operatorname { curl } \vec { F } ( 0,0,0 )$

Let F⃗=−3xzi⃗+4(y−x)j⃗+4xk⃗{ \vec { F } } = - 3 x z \vec { i } + 4 ( y - x ) \vec { j } + 4 x \vec { k }F=−3xzi+4(y−x)j​+4xk

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