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Vector equation of a line

  1. Jun 23, 2011 #1
    the equation of a straight line is given by 2x + y = 4

    (a) find the vector equation of a unit normal from the origin to the line and (b) the equation of a line passing through P(0,2) and normal to 2x + y = 4.


    i know i need to use the dot product some how but i am utterly confused as to where to begin! please help.

    i think first the vector equation for the given line is r = < 1 , -2 > then i need to dot r with rperp and set equal to 0? i am very confused. thanks!
     
  2. jcsd
  3. Jun 23, 2011 #2

    I like Serena

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    Welcome to PF, imb3cile! :smile:

    The general equation of a line is [itex](\vec n, \vec x) = d[/itex]
    In this equation [itex]\vec n[/itex] is a normal vector to the line, [itex]\vec x[/itex] is the vector with your coordinates x and y, and d is an arbitrary constant, that creates an offset to the origin.
    The parenthesis around the 2 vectors indicate that the dot product is taken.

    If the vector n would have components a and b, this would turn out as: ax + by = d

    Can you see from your own equation what the normal vector n would be?

    For part (a) you would need a multiple of this vector, such that if you fill it in for x and y, it matches the equation.
     
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