Two particles having position vectors $\vec{ r _{1}}=(3 \hat{ i }+5 \hat{ j }) m $ and $\vec{ r _{2}}=(-5 \hat{ i }-3 \hat{ j }) m $ are moving with velocities $\vec{ v _{1}}=(4 \hat{ i }+3 \hat{ j }) ms ^{-1}$ and $\vec{ v }_{2}=(a \hat{ i }+7 \hat{ j }) ms ^{-1}$. If they collide after $2\, s$, the value of $a$ is