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Line that intersects and is perpendicular to another line

  1. Sep 2, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the line through (4, 1, -1) that intersects and is perpendicular to the line
    x = -1 +t
    y = -2 + t
    z = 1 +t

    2. Relevant equations
    if they are perpendicular, the dot product of two vectors has to be zero.
    The book gives me another hint, if (x, y, z) is the point of intersection, find it's coordinates.

    3. The attempt at a solution
    The direction vector for the line l is <1, 1, 1>
    The vector for the line i'm trying to find is PQ = <(x-4), (y-1), (z+1)>
    if i do the dot product, i get
    (x-4)1 + (y-1)1 + (z+1)1 = 0.

    at this point, the only x, y and z i can think of to make the whole thing zero are (4,1,-1)....

    i am really confused on what i should do next.
  2. jcsd
  3. Sep 2, 2008 #2


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    Science Advisor
    Homework Helper

    Substitute the parametric form x=t-1 etc into the dot product equation. Find t.
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