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Calculus III, find shortest distance, 3 dimension problem? check my answer please?

  1. Dec 13, 2012 #1
    Calculus III, find shortest distance, 3 dimension problem? check my answer please??

    What is the shortest distance from the point P = (0, 1, 2) to the line given by l(t) = (1+t, 2-2t, 3+3t)?

    use distance formula

    d = sqrt ((x-0)^(2) + (y-1)^(2) + (z-2)^(2))

    d^(2) = ((x)^(2) + (y-1)^(2) + (z-2)^(2))

    substitute l(t) values

    =((1+t)^(2) + (1-2t)^(2) + (1+3t)^(2))

    simplify

    l ' (t) = 2 + 2t + 8t - 4 +6 + 18t

    = 2 + 2t + 8t - 4 + 6 + 18t

    =28t + 4

    4(1+7t) = 0

    t = - 1/7


    What do i do after i find the t value?
     
    Last edited: Dec 13, 2012
  2. jcsd
  3. Dec 13, 2012 #2

    LCKurtz

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    Re: Calculus III, find shortest distance, 3 dimension problem? check my answer please

    I didn't check your work, but the t value will tell you what point on the line is closest. Then what?
     
  4. Dec 13, 2012 #3
    Re: Calculus III, find shortest distance, 3 dimension problem? check my answer please

    nvm my whole answer is wrong. i used the wrong formula. i figured it out thanks.
     
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