# How do you find the unit vector for the following vector that connects (2,-5) and (0,3)?

Aug 28, 2017

$\hat{A B} = \frac{\hat{i} - 4 \hat{j}}{\sqrt{17}}$

#### Explanation:

$\vec{A} = 2 \hat{i} - 5 \hat{j}$
$\vec{B} = 3 \hat{j}$

Displacement vector $\vec{A B} = \vec{A} - \vec{B}$

$\vec{A B} = 2 \hat{i} - 5 \hat{j} - 3 \hat{j}$

$\vec{A B} = 2 \hat{i} - 8 \hat{j}$

$\vec{A B} = | \vec{A B} | \cdot \hat{A B}$

$\hat{A B} = \frac{\vec{A B}}{|} \vec{A B} |$

$\hat{A B} = \frac{2 \hat{i} - 8 \hat{j}}{\sqrt{68}}$

$\hat{A B} = \frac{\hat{i} - 4 \hat{j}}{\sqrt{17}}$