1. What is a Vector Between Two Points?

A vector between two points represents the direction and magnitude from the first point to the second point in 3D space. It's calculated by subtracting the coordinates of the starting point from the ending point.

2. How Does the Calculator Work?

The calculator uses the vector equation:

Where:

• \( (x_1, y_1, z_1) \) — Coordinates of the starting point
• \( (x_2, y_2, z_2) \) — Coordinates of the ending point
• \( \vec{v} \) — Resulting vector from point 1 to point 2

Explanation: The vector components represent the change in each coordinate direction needed to move from the first point to the second point.

3. Applications of Vectors

Details: Vectors between points are fundamental in physics (force, velocity), computer graphics, engineering, and navigation systems. They describe direction and magnitude between locations in space.

4. Using the Calculator

Tips: Enter the coordinates of both points in 3D space. The calculator will compute the vector components that take you from the first point to the second point.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between a point and a vector?
A: A point represents a specific location in space, while a vector represents direction and magnitude between points.

Q2: How do I find the magnitude of the vector?
A: The magnitude can be calculated using: \( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \)

Q3: Can I use this for 2D points?
A: Yes, just set the z-coordinates to 0 for both points.

Q4: What does a negative vector component mean?
A: It indicates direction opposite to that coordinate axis (negative x = left, negative y = down, negative z = backward).

Q5: How is this different from a position vector?
A: A position vector goes from the origin (0,0,0) to a point, while this calculates the vector between any two arbitrary points.