Two very thin metallic wires placed along X and Y-axis carry equal currents as shown here. AB and CD are lines at 45º  with the axes with origin of axes at O. The magnetic field will be zero on the line     

Every point on the line AB will be equidistant from X and Y-axis. So magnetic field at every point on the line AB due to wire 1 along X-axis is equal in magnitude but opposite in direction to the magnetic field due to wire along Y-axis. Hence