Components

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.

5 Must Know Facts For Your Next Test

1. A vector can be decomposed into its horizontal (x-axis) and vertical (y-axis) components using trigonometric functions.
2. 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.
3. 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.
4. Components are useful for adding and subtracting vectors graphically as they simplify complex vector operations into simpler arithmetic ones.
5. When combining multiple vectors, their respective components are added together to find the resultant vector’s components.

Review Questions

• How do you determine the x-component of a given vector?
• Why are components important when performing graphical methods of vector addition?
• What trigonometric functions are used to find the components of a vector?

Related terms

Vector: A quantity that has both magnitude and direction, represented by an arrow.

Resultant Vector: The single vector obtained from combining two or more vectors.

Trigonometric Functions: $\sin$, $\cos$, and $\tan$ functions used to relate angles to side lengths in right triangles.