When we have two vectors in physics, we often want to combine them in some way.  Often this involves adding the two together, but could involve subtracting them.  Before we go into the mathematical ways of combining vectors, let’s investigate vector addition through drawings.  We refer to these drawings as adding vectors graphically.

Adding vectors graphically: Getting from here to there

In a previous lesson, we saw the following picture, involving vectors position-and-displacement\(\color{black}{\vec{A}}\), \(\color{black}{\vec{d}}\), and \(\color{black}{\vec{B}}\).  If we started at the origin, followed vector \(\color{black}{\vec{A}}\), then followed vector \(\color{black}{\vec{d}}\), we would end up at point B.  This is the same location we would have ended up at if we had simply followed vector \(\color{black}{\vec{B}}\).

We could state this more clearly if we had simply said the following…

\(\color{black}{\vec{A}+\vec{d}=\vec{B}}\)

 

This notation really means what we said above.  It is just a whole lot easier to say.  Following one vector then another is like adding the two vectors together.

Notice that the length of vector B is shorter than the combined lengths of vector A and vector d.  This is a clue that we can’t just add vectors like we do numbers.  We will investigate this soon.