Answer
The magnitude of the minimum net force on particle 3 due to the other particles is zero.
Work Step by Step
When $0 \leq x \leq 5.0~m$, the vertical components of the forces cancel out.
When $0 \lt x \leq 5.0~m$, the horizontal components of the forces are directed in the positive direction of the x axis. Therefore, the net force on particle 3 is greater than zero.
However, when $x = 0$, there is no horizontal component of the forces on particle 3 due to the other particles. Therefore, the net force on particle 3 is zero.
There is a minimum at $x = 0$
Since the forces on particle 3 due to the other particles cancel out, the net force is zero.
The magnitude of the minimum net force on particle 3 due to the other particles is zero.
