1. ## 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

2. Originally Posted by overduex
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 $\displaystyle \vec a$ points at the point A and $\displaystyle \vec b$ points at the point B:

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

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

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

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

$\displaystyle \vec x = \left(\begin{array}{c}x\\y\end{array}\right) = \left(\begin{array}{c}2\\-1\end{array}\right) + r \cdot \left(\begin{array}{c}5\\-3\end{array}\right)~,~r \in \mathbb{R}$

3. Originally Posted by overduex
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
$\displaystyle \vec{OA} = \left( \begin{array}{c} 2 \\ -1 \end{array} \right)$ and $\displaystyle \vec{OB} = \left( \begin{array}{c} -3 \\ 2 \end{array} \right)$.
$\displaystyle \vec{AB} = \vec{AO} + \vec{OB} = -\vec{OA} + \vec{OB} = - \left( \begin{array}{c} 2 \\ -1 \end{array} \right) + \left( \begin{array}{c} -3 \\ 2 \end{array} \right) = \left( \begin{array}{c} -2 \\ 1 \end{array} \right) + \left( \begin{array}{c} -3 \\ 2 \end{array} \right)$
$\displaystyle = \left( \begin{array}{c} -5 \\ 3 \end{array} \right)$.