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Orthogonal vector equation (Ax=b)

  1. May 27, 2013 #1

    I'm having problems understanding vector representation in the form Ax=B could someone please point me in the right direction

    A vector equation for a given straight line is r = (i + 3j) + t(-i-j).
    i) Show that the point (1,2) does not lie on this line.
    ii) Construct a vector equation for the line that does go through the point (1;2), and is
    perpendicular to r.
    iii) Determine the point of intersection of the two lines.

    For i) i have set up parametric equations
    and substituted in x=1 and y=2
    t is not the same, therefore it does not lie on the line.
    For part ii) I have no idea on how to start I tried substituting t as 1 and then 2 which was wrong.
    I know that the dot product of two orthogonal vectors is 0

  2. jcsd
  3. May 27, 2013 #2


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    Gold Member

    In terms of the point (1,2) and any other general point (x,y) on the second line, can you find a vector (call it a) which is parallel to the line (i.e. it points in the same direction as the line)? Then, can you find a vector (call it b) that is parallel to the first line?

    These two vectors, a and b, should be orthogonal. As you pointed out, their dot product should be zero. Can you come up with an equation based on this?
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