# Magnitude of a vector

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### Examples

#### Lessons

1. Find the magnitude of the following vectors:

1. $\vec{p}$
2. $\vec{q}$
2. Find the magnitude of the following vectors:

1. $\vec{r}$
2. $\vec{s}$
3. Find the magnitude of the following vectors:
1. $\vec{m}=$< $3,-1$>

4. Given that the vector $\vec{v}$ has its initial point at (2,1) and its terminal point at (6,-4), find the magnitude of the vector $\vec{v}$

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###### Topic Basics
Finding the magnitude of a vector is very much the same as determining the length of the hypotenuse of a right triangle – we almost use the exact Pythagorean formula! In this section, we will learn how the horizontal component and the vertical component enable us to algebraically calculate the magnitude of a vector.
Magnitude of a vector
$|| \vec{v}||=\sqrt{v^2_x+v^2_y}$