LESSON 1: Vectors
A vector is a visual representation of magnitude and direction (it’s really just an arrow). For example,
when a boxer punches a punching bag, that punch has some amount of force and a direction. If we wanted to
analyze the boxer’s punch, we would use a vector (an arrow) to represent the boxer’s arm. Here is an example
of a vector with a force (or magnitude) of 80 N making a 30 degree angle with the x-axis:
This vector is two dimensional, so it can be broken into two component parts: the x-component and the y-
component. If this vector were drawn on a three dimensional graph it may have three components: the x-
component, y-component, and z-component. To break this vector into its component parts, we use the
trigonometry of a triangle. Remember these three formulas:
For this vector use the formula: sin(θ)=opp/hyp to find the y-component of the vector and the formula:
cos(θ)=adj/hyp to find the x-component of the vector.
So, this vector has a force of 40 N in the x-direction and a force of 69.282 N in the y-direction. In math, we
represent this vector with this notation:
So, the value before the “i” represents the force in the x-direction
and the value before the “j” represents the force in the y-direction.
If this vector were three dimensional it would also have a “k” value representing the value in the z-direction.
If you have had no previous experience with vectors hopefully this helped you gain a basic understanding
of the idea behind vectors. If you are still confused or don’t really understand, that is okay, you will
probably gain a better understanding of them as you progress through the next lessons. In the next lesson we
will explain how to take the magnitude of a vector. LESSON 1: Magnitude