Determine Whether the Vector Field Is Conservative $\overrightarrow { \mathrm { F } } ( x , y ) = \frac { 3 y } { x } \hat { \mathbf { i } } - \frac { x ^ { 3 } } { y ^ { 3 } } \hat { \mathbf { j } }$

question 87

Multiple Choice

Determine whether the vector field is conservative. If it is, find a potential function for the vector field. $\overrightarrow { \mathrm { F } } ( x , y ) = \frac { 3 y } { x } \hat { \mathbf { i } } - \frac { x ^ { 3 } } { y ^ { 3 } } \hat { \mathbf { j } }$

• A) conservative with potential function \(f ( x , y ) = \frac { 3 x ^ { 3 } } { y }\)
• B) conservative with potential function \(f ( x , y ) = \frac { x ^ { 3 } } { 3 y }\)
• C) conservative with potential function \(f ( x , y ) = \frac { x ^ { 3 } } { 4 y }\)
• D) conservative with potential function \(f ( x , y ) = \frac { 4 x ^ { 3 } } { y }\)
• E) not conservative

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