We know from Newton's second law of motion that Force = mass $\times$ acceleration. Acceleration can be expressed as velocity divided by time ($a = \frac{v}{T}$). Therefore, $F = m \times \frac{v}{T}$. Rearranging this formula to solve for mass ($m$), we get: $m = \frac{F \times T}{v} = F v^{-1} T$. Hence, the dimensional formula of mass in terms of $F$, $v$, and $T$ is $[F v^{-1} T]$.