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Math Help - IB Vectors

  1. #1
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    IB Vectors

    Find the position vectors that join the origin to the points with coordinates A(2, -1) and B(-3, 2). Express your answers as column vectors. Hence find line AB.


    All help is welcome
    Thanks in advance!
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  2. #2
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    Quote Originally Posted by overduex View Post
    Find the position vectors that join the origin to the points with coordinates A(2, -1) and B(-3, 2). Express your answers as column vectors. Hence find line AB.
    Vector \vec a points at the point A and \vec b points at the point B:

    \vec a=\left(\begin{array}{c}2\\-1\end{array}\right)

    \vec b=\left(\begin{array}{c}-3\\2\end{array}\right)

    The direction of the line AB is determined by \vec a - \vec b = \left(\begin{array}{c}5\\-3\end{array}\right)

    The line AB passes either through A or B. Therefore the equation of the line is:

    \vec x = \left(\begin{array}{c}x\\y\end{array}\right) = \left(\begin{array}{c}2\\-1\end{array}\right) + r \cdot \left(\begin{array}{c}5\\-3\end{array}\right)~,~r \in \mathbb{R}
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  3. #3
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    Quote Originally Posted by overduex View Post
    Find the position vectors that join the origin to the points with coordinates A(2, -1) and B(-3, 2). Express your answers as column vectors. Hence find line AB.


    All help is welcome
    Thanks in advance!
     \vec{OA} = \left( \begin{array}{c}<br />
2 \\<br />
-1 \end{array} \right)<br />
and \vec{OB} = \left( \begin{array}{c}<br />
-3 \\<br />
2 \end{array} \right)<br />
.

    \vec{AB} = \vec{AO} + \vec{OB} = -\vec{OA} + \vec{OB} = - \left( \begin{array}{c}<br />
2 \\<br />
-1 \end{array} \right) + \left( \begin{array}{c}<br />
-3 \\<br />
2 \end{array} \right) = \left( \begin{array}{c}<br />
-2 \\<br />
1 \end{array} \right) + \left( \begin{array}{c}<br />
-3 \\<br />
2 \end{array} \right)


     = \left( \begin{array}{c}<br />
-5 \\<br />
3 \end{array} \right).

    Earboth is obviously a quicker hand at latex than me. Note that his/her vector and mine are both in the direction of the line .... just in opposite directions. It doesn't matter which one you use.
    Last edited by mr fantastic; February 9th 2008 at 01:25 PM. Reason: Added the last paragraph
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