# 3-Dimensional Optimization

1. Nov 26, 2013

### infinitylord

I am completely self taught in Calculus, but I would like to have a better understanding of it before I go to College. I was looking up problems and came across this:
What is the distance d between the point A(2,-6,1) and the line l through B(3,4,-2) and C(7,-1,5)?

I attempted this by finding 3 slope formulas of the line between B and C in terms of alternating variables. (I already know this can't quite work, as the final formula will have multiple variables with no chance for substitution or elimination ). But nevertheless, I continued by creating a distance formula plugging in the slopes I got earlier for the x, y, and z variables. Remembering how to do optimization in single variable calculus, I took the derivative of the formula. I actually used a dell operator and set the numerator equal to zero. But this is definitely impossible. So now I need someone to help me out with this! Thanks!

2. Nov 26, 2013

### SteamKing

Staff Emeritus
Think instead about constructing a line passing thru point A which is perpendicular to the line passing thru B and C. Not every problem requires calculus to provide a solution.

3. Nov 26, 2013

### infinitylord

I understand what you mean. But how exactly do I do that?

4. Nov 26, 2013

### SteamKing

Staff Emeritus

5. Nov 26, 2013

### infinitylord

Unfortunately I tried to look it up before I posted on here. The Google skills are lacking with me. What Should I look up? Linear Algebra or vector calculus or something?

6. Nov 27, 2013

### SteamKing

Staff Emeritus
Google "distance from point to line"