# How do you find the magnitude of <5,6> and write it as a sum of the unit vectors?

Aug 5, 2017

$\text{magnitude} = 7.810$

$< 5 , 6 > = 5 \hat{i} + 6 \hat{j}$

#### Explanation:

We'll call the given vector $\vec{A}$ with components ${A}_{x} = 5$ and ${A}_{y} = 6$.

The magnitude of a vector is given by

|vecA| = sqrt((A_x)^2 + (A_y)^2) = sqrt(5^2 + 6^2) = color(blue)(ulbar(|stackrel(" ")(" "7.810" ")|)

$\text{ }$

Vectors in the notation $< x , y >$ can also be represented by unit vectors, with the unit vector $\hat{i}$ for the $x$-component and $\hat{j}$ for the $y$-component:

< 5,6 > = color(blue)(ulbar(|stackrel(" ")(" "5hati + 6hatj" ")|)