The formula to calculate the magnetic force acting on the wire is given by
F=IL×B...(1)
As the length of the wire is along positive x-axis, it can be written that
L=Li^...(2)
Substitute the expressions of the required parameters into equation (2) to obtain the force.
F==ILi^×(2i^+3j^−4k^)3ILk^+4ILj^...(3)
Hence, the magnitude of the force can be written as
F==(3IL)2+(4IL)25IL