1. A particle of mass 110 grams starts from rest and is acted upon by three forces, ${F}_{1}$,  ${F}_{2}$ and ${F}_{3}$,  given in vector form as

${F}_{1}=(\begin{matrix}1\\3\end{matrix})N{F}_{2}=(\begin{matrix}a\\-5\end{matrix})N{F}_{3}=(\begin{matrix}-3\\b\end{matrix})N$

where $a$ and $b$ are constants with  $a=\frac{4}{11}b$. 

Initially the particle is at rest and located at the origin.

Given that the position vector of the particle is  $(−55i−132j)m$  at time $T$ seconds,  where  $T>0$,  find the values of  $a$, $b$ and $T$.