Two similar current loop are placed with their axes along x-xis and y-axis respectively then the resultant magnetic field at a common point on the axis to the individual magnetic field at the same point is ..

The magnetic field will be zero at the resltant line between x and y axis. Every point on that line will be equidistant from X and Y axis. So, magnetic field on the line due to wire 1 along x axis is equal in magnitude but opposite in direction to the magnetic field along Y -axis, Hence net magnetic along the resultant line will be zero.