Test the vector field F to determine if it is conservative.
-$$F = \left( z e ^ { x + y } - \frac { 1 } { x } \right) i + z e ^ { x + y } j + e ^ { x + y } y _ { k }$$
A) Not conservative
B) Conservative

Question

Quizplus · Accepted Answer

The vector field is conservative because it is the gradient of the scalar potential function $f(x, y, z) = ze^{x+y} - \ln|x| + e^{x+y}$.

Test the Vector Field F to Determine If It Is F=(zex+y−1x)i+zex+yj+ex+yykF = \left( z e ^ { x + y } - \frac { 1 } { x } \right) i + z e ^ { x + y } j + e ^ { x + y } y _ { k }F=(zex+y−x1​)i+zex+yj+ex+yyk​

Test the Vector Field F to Determine If It Is $F = \left( z e ^ { x + y } - \frac { 1 } { x } \right) i + z e ^ { x + y } j + e ^ { x + y } y _ { k }$