A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by \(\mathbf{v}\) and the net is described by the given equations.
\(\mathbf{v}=\langle z y, x z, x yangle\), net given by \(y=1-x-z\), for \(x, y, z \geq 0\) oriented in the positive \(y\)-direction