Here, ${\overrightarrow F _{BC}} = \overrightarrow F$

$\because {\overrightarrow F _{AB}} = 0$

The net magnetic force on a current carrying closed loop in a uniform magnetic field is zero.

$\therefore {\overrightarrow F _{AB}} + {\overrightarrow F _{BC}} + {\overrightarrow F _{AC}} = 0$

$\Rightarrow {\overrightarrow F _{AC}} = - {\overrightarrow F _{BC}}$    ($\because$ ${\overrightarrow F _{AB}} = 0$)