# How do you find the magnitude of YZ given Y(3,1) and Z(0,4)?

Sep 23, 2016

"The Magnitude=3sqrt2~~4.242.

#### Explanation:

$Y \left(3 , 1\right) \mathmr{and} Z \left(0 , 4\right)$

$\therefore \vec{Y Z} = \left(0 , 4\right) - \left(3 , 1\right) = \left(0 - 3 , 4 - 1\right) , \text{ by Defn.} = \left(- 3 , 3\right) .$

Hence, magnitude of $\vec{Y Z} = | | \vec{Y Z} | | = \sqrt{{\left(- 3\right)}^{2} + {3}^{2}} = \sqrt{18} = 3 \sqrt{2}$

$\approx 3 \left(1.414\right) = 4.242$.