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Calculus III: Find a line perdendicular to XY-plane?

  1. Nov 13, 2012 #1
    The problem statement, all variables and given/known data[/b]
    "Find an equation for the line through the point P = (1, 0, −3) and perpendicular
    to the xy-plane,"

    obviously this includes vector <0, 0, 1>

    I am in Calc III and need help understanding how to do this TYPE of problem. Please include step-by-step instructions and any concepts used. Thank you.
     
  2. jcsd
  3. Nov 13, 2012 #2

    SteamKing

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    Why don't you try drawing a sketch? If a line is perpendicular to the x-y plane, how do the values of x and y change when the z-coordinate varies?
     
  4. Nov 13, 2012 #3

    haruspex

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    It does? Did you mean <1, 0, 0>?
    More generally, what can you say about the values of x and y on that line?
    I assume it's a vector equation you're after?
     
  5. Nov 13, 2012 #4
    Yes it's a vector equation I am after.

    my thought is: r = r0 + tv meaning r=<1,0,-3> + t<0,0,1>

    I just don't know if I'm right. Need clarification
     
  6. Nov 13, 2012 #5

    haruspex

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    Sure, or just r=<1,0,t-3>. But that's a parametric equation, which might not be what's wanted. Another form might be r x a = b, for some constant vectors a and b.
     
  7. Nov 13, 2012 #6
    Still highly confused.
     
  8. Nov 13, 2012 #7

    haruspex

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    Can you find constant vectors a and b such that the equation r x a = b implies r is of the form <1,0,*>?
     
  9. Nov 13, 2012 #8

    LCKurtz

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    Yes, that's exactly right. <1,0,-3> is a position vector to the point and <0,0,1> is a correct direction vector.
     
    Last edited: Nov 13, 2012
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