# How do you find the magnitude of <-2,4> and write it as a sum of the unit vectors?

Jan 8, 2017

$| \vec{r} | = 2 \sqrt{5}$

$< - 2 , 4 > = - 2 \hat{\vec{i}} + 4 \hat{\vec{j}}$

#### Explanation:

the magnitude of a vector $\vec{r} = \left(a \hat{\vec{i}} + b \hat{\vec{j}}\right)$

is: $| \vec{r} | = \sqrt{{a}^{2} + {b}^{2}}$

for $< - 2 , 4 > = - 2 \hat{\vec{i}} + 4 \hat{\vec{j}}$

$| \vec{r} | = \sqrt{{2}^{2} + {4}^{2}} = \sqrt{20} = 2 \sqrt{5}$