For the point P = (1,2,3) and the line x = 8-2t, y = -5+t, z = -4 + 3t

Find the distance between P and an arbitrary point on the line, in terms of the parameter t.

i chose t = 0 so the arbitrary point Q = (8,-5,-4)

then,

PQ = <7,-7,-7>

so the distance would be

$\displaystyle d = \sqrt(7^2 + 7^2 + 7^2) = \sqrt(147) $

Does this look correct?

Then the next part of this question states:

Find the value of t that minimizes the distance function above

i know that to find a minimization you take the derivative of the function but im not sure what to take the derivative of in this case.... or if thats what i even need to do.

Thanks for any help