Addition and Subtraction of Vectors in 1D

The tip-to-tail method is a visual way to add vectors. Place the tail of the second vector at the tip of the first vector. The sum is the vector from the tail of the first to the tip of the second.

Example 1: Both vectors point right

Add $\vec{x}_1 = 3$ and $\vec{x}_2 = 2$, both pointing right:

The top shows both vectors starting from the origin. The bottom shows the tip-to-tail construction: $\vec{x}_2$ starts where $\vec{x}_1$ ends. The purple resultant goes from start to finish: $\vec{x}_1 + \vec{x}_2 = 3 + 2 = 5$.

Example 2: Vectors point opposite directions

Add $\vec{x}_1 = 4$ (right) and $\vec{x}_2 = -3$ (left):

Move 4 units right, then 3 units left. The result: $\vec{x}_1 + \vec{x}_2 = 4 + (-3) = 1$, pointing right.

Example 3: Vertical vectors

Add $\vec{y}_1 = 3$ (up) and $\vec{y}_2 = -2$ (down):