Written by the Fiveable Content Team • Last updated August 2025
Written by the Fiveable Content Team • Last updated August 2025
Definition
Components are the individual parts of a vector that show its influence in different directions, typically along the x and y axes. They are essential for breaking down vectors to simplify analysis and calculations.
A vector can be decomposed into its horizontal (x-axis) and vertical (y-axis) components using trigonometric functions.
The x-component of a vector is found using $v_x = v \cos(\theta)$, where $v$ is the magnitude of the vector and $\theta$ is the angle with respect to the x-axis.
The y-component of a vector is found using $v_y = v \sin(\theta)$, where $v$ is the magnitude of the vector and $\theta$ is the angle with respect to the x-axis.
Components are useful for adding and subtracting vectors graphically as they simplify complex vector operations into simpler arithmetic ones.
When combining multiple vectors, their respective components are added together to find the resultant vector’s components.