1. What is Cross Product?

The cross product is a binary operation on two vectors in three-dimensional space. It results in a vector that is perpendicular to both original vectors, with magnitude equal to the area of the parallelogram they span.

2. How Does the Calculator Work?

The calculator uses the determinant 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: Cross products are used in physics (torque, angular momentum), computer graphics (surface normals), engineering (moment of force), and more.

4. Using the Calculator

Tips: Enter the components of both vectors. The calculator will compute the cross product vector, which will be perpendicular to both input vectors.

5. Frequently Asked Questions (FAQ)

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

Q2: What does the magnitude of the cross product represent?
A: It 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 in 3D. In 2D, the cross product is a scalar (the area).

Q4: What's the right-hand rule?
A: A mnemonic to determine the direction of the cross product vector. Point fingers in direction of A, curl towards B, thumb points in A×B direction.

Q5: Can the cross product be zero?
A: Yes, when vectors are parallel or one is zero, the cross product is the zero vector.