Question

Find the point on the line (5,2,3)+t(2,3,1) closest to the point M(1,-1,-2)

Answer 1

Hm. So you want to get these three equations as close as possible to true:

5 + 2t = 1
2 + 3t = -1
3 + t = -2

Basically, you want to minimize:

5 + 2t - 1
2 + 3t + 1
3 + t + 2

To be as close to 0 as possible.

Does that help?

Answer 2

Yes, thanks.