Infinity wire carrying current along i^j^k direction
- The current is flowing along the direction i^j^k through an infinite wire passing through the origin.
- This means the wire lies along the x-axis, y-axis, and z-axis.

Calculating the magnetic field at point (1,1,1)
- To find the magnetic field at point (1,1,1) due to the infinite wire, we can use the Biot-Savart law.
- The Biot-Savart law states that the magnetic field dB at a point due to a current element Idl is given by:
dB = (μ₀/4π) * (Idl x r) / r^3
where μ₀ is the permeability of free space, Idl is the current element, r is the distance from the current element to the point, and x denotes the cross product.

Direction of the magnetic field
- Since the current is along the i^j^k direction, the magnetic field will be perpendicular to both the current direction and the vector pointing from the wire to the point (1,1,1).
- Therefore, the magnetic field will be along the diagonal direction at point (1,1,1).

Calculating the magnitude of the magnetic field
- By using the Biot-Savart law and integrating over the entire length of the wire, we can find the total magnetic field at point (1,1,1).
- The magnitude of the magnetic field will depend on the current flowing through the wire and the distance to the point.

Conclusion
- In conclusion, the magnetic field at point (1,1,1) due to the infinite wire carrying current along the i^j^k direction can be calculated using the Biot-Savart law. The direction of the magnetic field will be diagonal, and its magnitude will depend on the current and distance to the point.