1. What is Vector Cross Product?

The cross product is a binary operation on two vectors in three-dimensional space that results in another vector perpendicular to both original vectors. It has important applications in physics, engineering, and computer graphics.

2. How Does the Calculator Work?

The calculator uses the cross product formula:

Where:

• \( A = (A_x, A_y, A_z) \) — First vector components
• \( B = (B_x, B_y, B_z) \) — Second vector components
• \( × \) — Cross product operator

Explanation: The result is a new vector perpendicular to both A and B, with magnitude equal to the area of the parallelogram formed by A and B.

3. Applications of Cross Product

Details: Cross products are used in calculating torque, angular momentum, surface normals in 3D graphics, and determining if two vectors are parallel.

4. Using the Calculator

Tips: Enter all six components (x,y,z for both vectors). The calculator will compute the resulting vector's components.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between dot product and cross product?
A: Dot product gives a scalar quantity, while cross product gives a vector perpendicular to both input vectors.

Q2: What does a zero cross product mean?
A: A zero cross product indicates that the vectors are parallel (or at least one is zero).

Q3: Can you compute cross product in 2D?
A: In 2D, cross product is treated as a scalar (z-component of 3D cross product with z=0).

Q4: What's the right-hand rule?
A: It's a mnemonic for determining the direction of the cross product vector (point fingers along A, curl toward B, thumb points to A×B).

Q5: Is cross product commutative?
A: No, A×B = -B×A (anti-commutative).