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Calculus

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Find the distance from point P<5,5,2> to the line x=0 , y=5-5t, z=2+t.


I keep getting 0 and that's not the correct answer and I can't figure out what's going wrong.

  • Calculus - ,

    Expressed in terms of the paratmer t, the squared distance from P to any point on the line is
    D^2 = (x1-x2)^2 + (y1-y2)^2 +(z1-z2)^2
    =5^2 + (5-5t-5)^2 + (2+t-2)^2
    = 25 + 25t^2 + t^2 = 26 t^2 + 25

    Differentiate with respect to t and set the derivative equal to zero to find where the distance is a minimum
    52t = 0
    t = 0
    At that value of t, the distance^2 is
    D^2 = 25
    so D = 5

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