The magnitude of a vector is the amount of force the vector has. Referring back to the analogy with
the boxer punching a punching bag, the magnitude of the boxer’s punch would be how hard he hit the
bag. Let’s take the magnitude of this vector:
When you take the magnitude of a vector, you are essentially just using Pythagorean’s right triangle
rule. The “i” value is one leg of a right triangle, the “j” value is the other leg of the right triangle,
and the hypotenuse is the magnitude. Using this formula to find the magnitude will work for all two
dimensional vectors: (note: the magnitude of a vector is represented by "| |" )
Finding the magnitude of three dimensional vectors is essentially the same as finding the magnitude of
two dimensional vectors, except with the added “k” value. Here is an example of a three dimensional
vector and its magnitude:
In the next section we will cover unit vectors. In order to find the unit vector of a vector you need to
know how to find its magnitude. So it may be best to keep this lesson in mind while moving to the next
section. Lesson 1: Unit Vector