Find an equation of the plane passing through the three points given. \(P = (2, 0, 0),\)

\(Q = (0, 4, 0),\)

\(R = (0, 0, 2)\)

Let \(v = zk\) be the velocity field of a fluid in \(\displaystyle{R}^{{3}}\). Calculate the flow rate through the upper hemisphere \((z > 0)\) of the sphere \(\displaystyle{x}^{{2}}+{y}^{{2}}+{z}^{{2}}={1}.\)

Consider the line represented by the equation \(5x + 2y = 10\). How is the slope of the line related to values of A, B, and C in standard form \(Ax + By = C\)?