Let $\vec { F } = \left( - 2 x ^ { 2 } - a x z \right) \vec { i } + \left( b x ^ { 2 } + 16 \right) \vec { j } + ( x + c y ) \vec { k }$ be a smooth vector field with $\operatorname { curl } \overrightarrow { \vec { F } } ( 1 , - 4,4 ) = - 3 \vec { i } + 3 \vec { j } + 8 \vec { k }$ Determine the values of a, b and c.

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The Answer of Let $\vec { F } = \left( - 2 x ^ { 2 } - a x z \right) \vec { i } + \left( b x ^ { 2 } + 16 \right) \vec { j } + ( x + c y ) \vec { k }$ be a smooth vector field with $\operatorname { curl } \overrightarrow { \vec { F } } ( 1 , - 4,4 ) = - 3 \vec { i } + 3 \vec { j } + 8 \vec { k }$ Determine the values of a, b and c.

Let F⃗=(−2x2−axz)i⃗+(bx2+16)j⃗+(x+cy)k⃗\vec { F } = \left( - 2 x ^ { 2 } - a x z \right) \vec { i } + \left( b x ^ { 2 } + 16 \right) \vec { j } + ( x + c y ) \vec { k }F=(−2x2−axz)i+(bx2+16)j​+(x+cy)k

Let $\vec { F } = \left( - 2 x ^ { 2 } - a x z \right) \vec { i } + \left( b x ^ { 2 } + 16 \right) \vec { j } + ( x + c y ) \vec { k }$