# How do you find the component form and magnitude of the vector v given initial point (-2,7) and terminal point (5,-17)?

Jun 5, 2017

The vector is $= 7 \vec{i} - 24 \vec{j}$ and the magnitude is $= 25$

#### Explanation:

Let the point $A = \left(- 2 , 7\right)$

and $B = \left(5 , - 17\right)$

Then,

$\vec{A B} = \left(\begin{matrix}5 - \left(- 2\right) \\ - 17 - 7\end{matrix}\right) = \left(\begin{matrix}7 \\ - 24\end{matrix}\right)$

The magnitude of $\vec{A B}$ is

$| | \vec{A B} | | = \sqrt{{\left(7\right)}^{2} + {\left(- 24\right)}^{2}} = 25$