1. What is Vector Product?

The vector product (or 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), and engineering (moment of force calculations).

4. Using the Calculator

Tips: Enter the i, j, k components for both vectors. The calculator will compute the perpendicular vector using the right-hand rule.

5. Frequently Asked Questions (FAQ)

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

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 gives a scalar (the z-component of what would be a 3D result).

Q4: What is the right-hand rule?
A: Point fingers in direction of first vector, curl towards second vector - thumb points in cross product direction.

Q5: Can I calculate cross product for 2D vectors?
A: Yes, treat them as 3D vectors with z=0. The result will have only a z-component.