At time $t=0,$ a particle is located at the point $(5,7,3).$ It travels in a straight line to the point $(2,8,6),$ has speed $5$ at $(5,7,3)$ and constant acceleration $-3i+j+3k.$ Find an equation $1$ position vector $r(t)$ of the particle at time $t.$

The equation for the position vector $r(t)$ of the particle at time $t$ is $r(t)=(\sqrt[\phantom{2}]{-3})i+(\sqrt[\phantom{2}]{1})j+(\sqrt[\phantom{2}]{3})k.$

$($Type exact answers, using radicals as needed.$)$