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's widely used in physics, engineering, and computer graphics.

2. How Does the Calculator Work?

The calculator uses the standard cross product formula:

Which expands to:

• \( x \)-component: \( A_yB_z - A_zB_y \)
• \( y \)-component: \( A_zB_x - A_xB_z \)
• \( z \)-component: \( A_xB_y - A_yB_x \)

3. Applications of Cross Product

Details: The cross product is essential for calculating torque, angular momentum, surface normals in 3D graphics, and determining if vectors are parallel.

4. Using the Calculator

Tips: Enter the x, y, and z components for both vectors A and B. The calculator will compute the resulting perpendicular vector.

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 the vectors are parallel or at least one is a zero vector.

Q3: What's the right-hand rule?
A: It's a mnemonic for determining the direction of the cross product vector - point fingers in direction of A, curl toward B, thumb points in result direction.

Q4: Can cross product be used in 2D?
A: In 2D, the cross product is treated as a scalar (z-component of the 3D result with z=0).

Q5: What are some real-world applications?
A: Calculating torque in physics, determining surface orientation in computer graphics, and finding normal vectors in 3D modeling.