Vector Addition

Imagine traveling from point $A$ to point $B$, represented by the vector $\overrightarrow{AB}$. Then, you continue traveling from point $B$ to point $C$, represented by the vector $\overrightarrow{BC}$. The overall journey from $A$ to $C$ can be represented by the vector $\overrightarrow{AC}$.

If you want to travel from point $A$ to $C$, you could either:

• Travel along the vector $\overrightarrow{AC}$, or
• Travel along the vector $\overrightarrow{AB}$ and then along the vector $\overrightarrow{BC}$

This head-to-tail combination of vectors is what we call vector addition, and in this case it would make sense to be able to say that the combination $\overrightarrow{AB} + \overrightarrow{BC}$ is equivalent to the vector $\overrightarrow{AC}$.

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