2D Vectors: Operations

When you move through space, you often make multiple displacements. For example, you might move $4$ units right and $1$ unit ahead, then continue with another displacement of $2$ units right and $3$ units ahead. What is your total displacement from your starting point?

This is exactly what vector addition helps us determine. Just as scalars can be added together, vectors can also be combined through addition to find a resultant vector.

The Tip-to-Tail Method

The most intuitive way to visualize vector addition is through the tip-to-tail method. To add two vectors $\vec{a}$ and $\vec{b}$:

1. Draw the first vector $\vec{a}$ starting from the origin
2. Place the tail of the second vector $\vec{b}$ at the tip of the first vector
3. The resultant vector $\vec{R} = \vec{a} + \vec{b}$ is drawn from the origin to the tip of the second vector