Question

Find the distance between point P(1,2,5) and line x=t, y=1+t, z=2t.

Answer 1

Use the distance formula, which will give you distance as a function of t, then minimize that function (find the value of t that minimizes the function, and the value of the function). I would probably minimize the square of the distance to make the calculations easier.

Answer 2

Good plan, but I'm not sure how to apply this formula. Can you guide me?

Answer 3

\[(d(t))^2=(t-1)^2+(t-1)^2+(2t-5)^2=6t^2-24t+27\]This function has its minimum of three at t=2, so the distance is sqrt 3.

Answer 4

Ah I see. Thanks!

Answer 5

Just need a little nudge, that's all. Thanks!

Answer 6

No sweat. Do math every day.