Vectors and Parametric Equations
PhD. in Mathematics
Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.
In order to understand the significance of a force vector we must understand the components of force. The components of a force can be seen with horizontal and vertical change when looking at the geometric representation or as the numbers in the algebraic representation. The components of a force represent the combined vertical and horizontal forces that combine to make the resultant force.
I want to talk about components of a vector. Components are two vectors that add up to the given vector which are perpendicular to each other so let's start with an example.
Here's a say a force vector, I can draw two components which are two other vectors that add up to my force f so these two work right I'm drawing them from head to tail so you can see they add up to force f and they're perpendicular so those are the only two requirements for vectors to be components let's call this vector a and this one b so we see that a+b=f so that's the one requirement for components. The two components have to add up to the original vector and the other one is that the two are perpendicular a and b are perpendicular, sometimes called orthogonal when you're talking about vectors. Okay, but one of the things that we're going to need to be able to do is to find horizontal and vertical components, so those are very specific components and of course when you, you're guaranteed to get components if you take a horizontal and vertical vector that add up to your original vector f so let's call this one h and this one v it's clear here that h plus v also equals f right in both of these pictures these are the same forces but you can see that I have two different sets of components here and then h and v are of course perpendicular, so again two the two requirements for components are that the vectors add up to your original vector f and that they're perpendicular to each other we've been finding components in this lesson.