1. What Is A Directed Line Segment?

A directed line segment represents a vector with both magnitude and direction, defined by its starting and ending points in coordinate space.

2. How Does The Calculator Work?

The calculator uses the vector formula:

Where:

• \( (x_1, y_1, z_1) \) — Starting point coordinates
• \( (x_2, y_2, z_2) \) — Ending point coordinates
• \( \vec{V} \) — Resulting vector

Explanation: The vector represents the displacement from the start point to the end point, with components in each coordinate direction.

3. Importance Of Vector Calculation

Details: Vector calculations are fundamental in physics, engineering, computer graphics, and many scientific fields for representing direction and magnitude.

4. Using The Calculator

Tips: Enter coordinates for both start and end points. The calculator supports 3D coordinates (x, y, z). All values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between a vector and a directed line segment?
A: A directed line segment is a geometric representation of a vector, showing both magnitude and direction from a specific starting point.

Q2: Can I use this for 2D calculations?
A: Yes, simply set the z-coordinate to 0 for both start and end points for 2D vector calculations.

Q3: What does a negative vector component mean?
A: Negative components indicate direction opposite to the positive coordinate axis direction.

Q4: How is vector magnitude calculated?
A: Magnitude = √(x² + y² + z²), but this calculator only provides the vector components.

Q5: Can I calculate multiple vectors?
A: This calculator computes one vector at a time. For multiple vectors, perform separate calculations.