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Homework Help: Distance from a point in space to a plane given a perpendicular line

  1. May 20, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the distance from the point A = (1; 0; 2) to the plane passing through the point (1; 2; 1) and perpendicular to the line given by the parametric equations x = 7, y = 1 + 2t, z = t - 3.

    2. Relevant equations

    d = | (PS dot n)/|n||

    3. The attempt at a solution

    Set n = <0, 2, 1> from the line given

    |n|= sqrt(5)

    I am confused about finding the S point. Would the second point be the one that passes through the plane?

    If so,

    PS = <0, -2, -1> so PS dot n = <0, -4, -1> and it would become something like -4/sqrt(5) + -1/sqrt(5). I get -5sqrt(5)/5 which becomes |-sqrt(5)|.

    In general, when do we use intercepts (recommended by the textbook) and how vs just the point on the plane?
  2. jcsd
  3. May 20, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    S is any point on the plane. Since you were given (1,2,1) just use it.

    Check your signs on PS.

    I guess it depends on what problem you are solving. Just fix your arithmetic and you should be OK here.
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