Given $\operatorname { curl } { \vec { F } } = 10 x y z \vec { i } + \left( a y ^ { 2 } z + 2 b y z \right) \vec { j } - 4 z ^ { 2 } \vec { k }$ , find the values of the constants a and b, without knowing the expression of $\vec { F }$ .

Question

Given $\operatorname { curl }  { \vec { F } } = 10 x y z \vec { i } + \left( a y ^ { 2 } z + 2 b y z \right) \vec { j } - 4 z ^ { 2 } \vec { k }$ , find the values of the constants a and b, without knowing the expression of $\vec { F }$ .

Quizplus · Accepted Answer

The Answer of Given $\operatorname { curl }  { \vec { F } } = 10 x y z \vec { i } + \left( a y ^ { 2 } z + 2 b y z \right) \vec { j } - 4 z ^ { 2 } \vec { k }$ , find the values of the constants a and b, without knowing the expression of $\vec { F }$ .

Given curl⁡F⃗=10xyzi⃗+(ay2z+2byz)j⃗−4z2k⃗\operatorname { curl } { \vec { F } } = 10 x y z \vec { i } + \left( a y ^ { 2 } z + 2 b y z \right) \vec { j } - 4 z ^ { 2 } \vec { k }curlF=10xyzi+(ay2z+2byz)j​−4z2k

Given $\operatorname { curl } { \vec { F } } = 10 x y z \vec { i } + \left( a y ^ { 2 } z + 2 b y z \right) \vec { j } - 4 z ^ { 2 } \vec { k }$