1. What is a Normal Vector?

A normal vector is a vector that is perpendicular to a surface. For three points in 3D space, the normal vector is calculated as the cross product of two vectors formed by these points.

2. How Does the Calculator Work?

The calculator uses the cross product formula:

Where:

• \( P1, P2, P3 \) — Three points in 3D space
• \( \times \) — Cross product operator
• \( \vec{n} \) — Resulting normal vector

Explanation: The calculator first creates two vectors from the three points (P2-P1 and P3-P1), then computes their cross product to get the normal vector.

3. Importance of Normal Vectors

Details: Normal vectors are essential in computer graphics (for lighting calculations), physics (for collision detection), and engineering (for surface analysis).

4. Using the Calculator

Tips: Enter the x, y, z coordinates for each of the three points. The calculator will compute the normal vector that is perpendicular to the plane formed by these points.

5. Frequently Asked Questions (FAQ)

Q1: What does the normal vector represent?
A: It represents the direction perpendicular to the plane formed by the three input points.

Q2: How is the direction of the normal vector determined?
A: The direction follows the right-hand rule based on the order of the points (P1→P2→P3).

Q3: What if all three points are colinear?
A: The normal vector will be [0, 0, 0] since colinear points don't define a unique plane.

Q4: Can I normalize the resulting vector?
A: Yes, you can divide each component by the vector's magnitude to get a unit normal vector.

Q5: What applications use normal vectors?
A: Computer graphics (lighting/shading), physics simulations, CAD software, and geometric analysis.