Two straight wires perpendicular to the plane of this page are shown in the figure. The currents in the wires are the same. The Current in M Is out of the page and The Current In N Is into the page. The Vector that represent the resultant magnetic field at point P is

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To find the vector that represents the resultant magnetic field at point P, we need to use the right-hand rule for determining the direction of the magnetic field due to a current-carrying wire.

In this case, both wires have currents flowing through them in different directions. The current in wire M is out of the page, while the current in wire N is into the page.

To apply the right-hand rule, you can follow these steps:

1. Start by placing your right hand flat on the page, with your thumb pointing away from you (out of the page) in the direction of the current in wire M. This represents the direction of the magnetic field due to wire M at point P.

2. Next, curl your fingers towards wire N, which has a current into the page. The direction in which your fingers curl represents the direction of the magnetic field due to wire N at point P.

3. Finally, the resultant magnetic field vector at point P is the vector sum of the individual magnetic fields caused by each wire. To find its direction, use the right-hand rule again. Place your right hand flat on the page, with your thumb pointing in the direction of the magnetic field due to wire M (away from you, out of the page). Curl your fingers towards the direction of the magnetic field due to wire N. Your extended thumb will now indicate the resultant magnetic field at point P.

Please note that without specific numerical values for the currents and distances, we cannot determine the magnitude or exact direction of the resultant magnetic field vector at point P in this specific case. The provided image only shows the relative orientations of the wires, not their distances or the scale of the diagram.