# How do you find the component form and magnitude of the vector v given initial point (-3,-5) and terminal point (5,1)?

Dec 9, 2017

The component form is $= 8 \vec{i} + 6 \vec{i}$ and the magnitude is $= 10$

#### Explanation:

Let the point $A = \left(- 5 , - 5\right)$ and the point $B = \left(5 , 1\right)$

Then the vector

$\vec{v} = \left(B\right) - \left(A\right) = \left(\begin{matrix}5 \\ 1\end{matrix}\right) - \left(\begin{matrix}- 3 \\ - 5\end{matrix}\right) = \left(\begin{matrix}8 \\ 6\end{matrix}\right) = < 8 , 6 > = 8 \vec{i} + 6 \vec{i}$

The magnitude of $\vec{v}$ is

$| | \vec{v} | | = \sqrt{{8}^{2} + {6}^{2}} = \sqrt{64 + 36} = \sqrt{100} = 10$