A particle travels in $R^3$ via the linear motion

$l(t)=(-5,7,-2)+t*(-5,-4,-3)$

Determine the time and location of the particle when it is at closest proximity to the point $Q(3,14,17).$

Time of closest proximity:

Location of closest proximity:

Closest distance:

Hint type $\sqrt[\phantom{2}]{5}$ as sqrt$(5)$