A bar magnet is centered at the origin with its longitudinal axis aligned along the \(x\)-axis. The magnet has its south pole located at \(x = -d\) and its north pole located at \(x = +d\). Three locations are identified: Point \(P_1\) at \((2d, 0)\), Point \(P_2\) at \((0, 2d)\), and Point \(P_3\) at the origin \((0, 0)\) inside the magnet. Which of the following correctly indicates the direction of the magnetic field vector \(\vec{B}\) at points \(P_1\), \(P_2\), and \(P_3\)?