# How do you find the magnitude of <2.5,6> and write it as a sum of the unit vectors?

Sep 3, 2017

$\therefore < 2.5 , 6 > = 2.5 \hat{i} + 6 \hat{j} .$

$| | < 2.5 , 6 > | | = \sqrt{{\left(2.5\right)}^{2} + {6}^{2}} = \sqrt{6.25 + 36} = \sqrt{42.25} = 6.5 .$

#### Explanation:

$< 2.5 , 6 > = < 2.5 , 0 > + < 0 , 6 > ,$

$= 2.5 < 1 , 0 > + 6 < 0 , 1 > ,$

$\therefore < 2.5 , 6 > = 2.5 \hat{i} + 6 \hat{j} .$

$| | < 2.5 , 6 > | | = \sqrt{{\left(2.5\right)}^{2} + {6}^{2}} = \sqrt{6.25 + 36} = \sqrt{42.25} = 6.5 .$