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Vector Equations of Lines

  1. Aug 29, 2008 #1

    Find the parametric equations of the lines L1, L2, L3 and L4 that pass through the indicated verticies of the square:

    [​IMG]


    This isn't a homework question but I need some tutoring help here with parametric equations of lines, those who are good at linear algebra. Thanks.




    3. The attempt at a solution

    L1 for example, is parallel to the y-axis a vector that's (0,1)

    A vector equation of the line is x=tv. If we let x = (x,y) this equation can be expressed in the component form as;

    (x,y) = t(0,1)

    (t is some scalar.)

    Therefore the parametric equation has to be:

    x = t.0
    y = t

    [tex]\Rightarrow x = 0, y = t[/tex]

    But the correct answer in the textbook suggests: L1: x = 1, y = t

    Why did I get the wrong answer for x?

    I'm pretty confused right now I've been reading the book this afternoon and I still don't get it, I’m too tired to continue, I’m off to bed now!
     
  2. jcsd
  3. Aug 30, 2008 #2

    danago

    User Avatar
    Gold Member

    You are right that L1 is parallel to the vector (0,1), but when t=0, your equation suggest that (x,y)=(0,0) which cannot be correct, since the line does not pass through the origin. Can you see the detail you have overlooked?
     
  4. Aug 30, 2008 #3

    Defennder

    User Avatar
    Homework Helper

    No it isn't. A vector equation is of the form [tex]\vec{OR} + t\vec{v}[/tex]. Assuming that you meant that the x-component of the line is x=tv where v is a vector, it's still incorrect because x is constant for L1, and doesn't vary for any parameter t.
     
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