2D Vectors: Components and Unit Vectors

In $1\text{D}$ motion, a single number (positive or negative) describes displacement. Real motion, however, often happens in two dimensions — like a ball kicked across a field or a drone flying overhead.

For motion in a plane, we need two numbers: displacement in the $x$-direction and displacement in the $y$-direction. A 2D vector captures both.

Components of a 2D Vector

A 2D vector has two components:

• $x$-component: horizontal displacement
• $y$-component: vertical displacement

Consider a displacement vector $\vec{d}$ pointing from the origin to the coordinate $(3, 2)$:

We write $\vec{d} = (3, 2)$, meaning $3$ units along the $x$-axis and $2$ units along the $y$-axis. The components are $d_x = 3$ and $d_y = 2$.

Breaking Down the Vector

The vector can be decomposed into its $x$ and $y$ components: