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

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