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3-Dimensional Optimization

  1. Nov 26, 2013 #1
    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!
     
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  3. Nov 26, 2013 #2

    SteamKing

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    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.
     
  4. Nov 26, 2013 #3
    I understand what you mean. But how exactly do I do that?
     
  5. Nov 26, 2013 #4

    SteamKing

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    Google is your friend.
     
  6. Nov 26, 2013 #5
    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?
     
  7. Nov 27, 2013 #6

    SteamKing

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    Google "distance from point to line"
     
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