# Thread: vector equation

1. ## vector equation

Hello,

Find the vector equation for the lines joining (3,7) , (5,4)

Thanks in advance.

2. Originally Posted by Oasis1993
Hello,

Find the vector equation for the lines joining (3,7) , (5,4)

Thanks in advance.

$slope = \frac{7-4}{3-5} = \frac{3}{-2}$

vector equation

$\frac{y-4}{x-5} = \frac{-3}{2}$

$2(y-4) = -3(x-5)$

$2y-8 = -3x+15$

$y = \frac{-3x +15 +8 }{2}$

3. Originally Posted by Oasis1993
Hello,

Find the vector equation for the lines joining (3,7) , (5,4)

Thanks in advance.
the direction vector is $(5,4) - (3,7) = (2,-3)$

the parametric equation in vector form for this line is $\left(
\begin{array}
[c]{c}%
x\\
y
\end{array}
\right) = \left(
\begin{array}
[c]{c}%
3\\
7
\end{array}
\right) + \left(
\begin{array}
[c]{c}%
2\\
-3
\end{array}
\right)t$
, $t \in \mathbb{R}$