Test the vector field F to determine if it is conservative.
-$$\mathbf { F } = 4 x ^ { 3 } y ^ { 4 } z ^ { 4 } i + 4 x ^ { 4 } y ^ { 3 } z ^ { 4 } j + 4 x ^ { 4 } y ^ { 4 } z ^ { 3 } k$$
A) Not conservative
B) Conservative

Question

Quizplus · Accepted Answer

A vector field $\mathbf{F}$ is conservative if its curl is zero. The curl of $\mathbf{F}$ is given by $\nabla \times \mathbf{F}$. Calculating the curl for the given $\mathbf{F}$, we find that it is indeed zero, which means that $\mathbf{F}$ is conservative.

Test the Vector Field F to Determine If It Is F=4x3y4z4i+4x4y3z4j+4x4y4z3k\mathbf { F } = 4 x ^ { 3 } y ^ { 4 } z ^ { 4 } i + 4 x ^ { 4 } y ^ { 3 } z ^ { 4 } j + 4 x ^ { 4 } y ^ { 4 } z ^ { 3 } kF=4x3y4z4i+4x4y3z4j+4x4y4z3k

Test the Vector Field F to Determine If It Is $\mathbf { F } = 4 x ^ { 3 } y ^ { 4 } z ^ { 4 } i + 4 x ^ { 4 } y ^ { 3 } z ^ { 4 } j + 4 x ^ { 4 } y ^ { 4 } z ^ { 3 } k$