1. What is the Cross Product?

The cross product is a binary operation on two vectors in three-dimensional space that results in a vector perpendicular to both original vectors. It has 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
• \( A \times B \) — Resulting perpendicular vector

Explanation: The cross product magnitude equals the area of the parallelogram formed by the two vectors, and its direction follows the right-hand rule.

3. Importance of Cross Product

Details: The cross product is essential for calculating torque, angular momentum, surface normals in 3D graphics, and determining perpendicular vectors in physics and engineering applications.

4. Using the Calculator

Tips: Enter all six components (x,y,z for both vectors). The calculator will compute the resulting vector components using the cross product formula.

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 the cross product magnitude represent?
A: The magnitude equals the area of the parallelogram formed by the two vectors.

Q3: Why is the cross product only defined in 3D?
A: The perpendicular vector concept only works consistently in three dimensions, though 7D has a similar operation.

Q4: How is the direction of the result determined?
A: By the right-hand rule - point fingers in A's direction, curl towards B, thumb points in A×B direction.

Q5: What happens if vectors are parallel?
A: The cross product is the zero vector (0,0,0) when vectors are parallel.