Answer
Not Conservative
Work Step by Step
As we know that $\text{curl} F =(\dfrac{\partial R}{\partial y}-\dfrac{\partial Q}{\partial z})i +(\dfrac{\partial P}{\partial z}-\dfrac{\partial R}{\partial x}) k+(\dfrac{\partial Q}{\partial x}-\dfrac{\partial P}{\partial y})k $
A vector field is conservative iff the $\text{curl} F =0$
Given: $F=(z+y) i+zj+(y+x) k$
Now, curl F$=(1-1) i+(1-1)j +(0-1) k$
and $-k \ne 0$
This shows that the vector field is Not Conservative.
