Magnitude Examples

What is the magnitude of the vector <3, 4>?

We can draw this vector as an arrow:

Using the Pythagorean Theorem, we find the magnitude of the vector:

Find the magnitude of the vector <-2, 3>.

Here's an incorrect answer. Using the Pythagorean Theorem, the magnitude of this vector is 

That's incorrect because we didn't square -2. We squared 2 and ended up with an incorrect negative sign. 

Here's the right answer. Using the Pythagorean Theorem, the magnitude of this vector is 

Here's an alternate approach:

Since (-2)² equals 2², the magnitude of the vector <-2,3> is the same as the magnitude of the vector <2,3>, which is 

Find the magnitude of the vector <0, 7>.

This vector lies flat along the y-axis and has length 7: 

Therefore || <0,7> || = 7.