Consider the vector . Let’s say that . How far is from the origin?
To find the distance between the origin (the vector ) and we can use Pythagoras’ theorem.
How about if we want to find the distance between the vector and another vector ? What we can do is find the vector between the two points (this is written as ), and then use Pythagoras’ theorem in the same way we did above?
First, we can draw a diagram:
We have no clue how to find the vector between and (). To find the vector between and can draw a diagram and think about what we do know. Remember that we can read as "move from the origin to " and as "move from the origin to ". Then, to move from to we want to move "from to the origin" and "from the origin to ". This is . To find the distance (aka magnitude of this vector), we just use Pythagoras’s theorem.
Therefore the distance between and is