1. What Are Vector Components?

Vector components are the projections of a vector along the axes of a coordinate system. Any 2D vector can be broken down into its x (horizontal) and y (vertical) components, which are perpendicular to each other.

2. How Does the Calculator Work?

The calculator uses trigonometric functions to determine the components:

Where:

• \( |\vec{v}| \) — Magnitude of the vector
• \( \theta \) — Angle between the vector and positive x-axis (in degrees)
• \( x \) — Horizontal component (parallel to x-axis)
• \( y \) — Vertical component (parallel to y-axis)

Explanation: The cosine function gives the adjacent side (x-component) while the sine function gives the opposite side (y-component) of the right triangle formed by the vector.

3. Applications of Vector Components

Details: Vector components are essential in physics (force analysis), engineering (structural calculations), computer graphics (object movement), and navigation (direction finding).

4. Using the Calculator

Tips: Enter the vector magnitude (must be ≥0) and angle in degrees (can be negative or >360°). The angle is measured counterclockwise from the positive x-axis.

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is negative?
A: Negative angles are measured clockwise from the positive x-axis. The calculator handles them correctly.

Q2: What if my angle is greater than 360°?
A: The calculator automatically reduces angles modulo 360° (e.g., 450° becomes 90°).

Q3: How do I combine components back into a vector?
A: Use \( |\vec{v}| = \sqrt{x^2 + y^2} \) and \( \theta = \arctan(y/x) \) (with quadrant adjustment).

Q4: What coordinate system is this using?
A: Standard Cartesian coordinates with positive x to the right and positive y upwards.

Q5: Can I use this for 3D vectors?
A: This calculator is for 2D vectors only. 3D vectors require an additional angle (azimuth or elevation).