A wire carrying a current I along the positive x-axis has length L...

The formula to calculate the magnetic force acting on the wire is given by

$\overset{\to}{F} = I\overset{\to}{L} \times \overset{\to}{B} . . . \left(1\right)$

As the length of the wire is along positive x-axis, it can be written that

\overset{\to}{L} = L\overset{^}{i} . . . \left(2\right)

Substitute the expressions of the required parameters into equation (2) to obtain the force.

\begin{cases}\overset{\to}{F} & = & IL\overset{^}{i} \times \left(2\overset{^}{i} + 3\overset{^}{j} - 4\overset{^}{k}\right) \\ = & 3IL\overset{^}{k} + 4IL\overset{^}{j} . . . \left(3\right)\end{cases}

Hence, the magnitude of the force can be written as

$\begin{cases}F & = & \sqrt{{\left(3IL\right)}^{2} + {\left(4IL\right)}^{2}} \\ = & 5IL\end{cases}$