1. What Does Cross Product Calculate in Python?

The cross product is a binary operation on two vectors in three-dimensional space that results in a vector perpendicular to both original vectors. In Python, it's calculated using numpy.cross(A, B).

2. How Does numpy.cross() Work?

The numpy.cross() function computes the cross product of two vectors:

Where:

• \( A \) — First input vector (2D or 3D)
• \( B \) — Second input vector (must match dimension of A)

Note: For 2D vectors, the function returns the z-coordinate of the cross product (as a scalar).

3. Mathematical Definition

For 3D vectors \( A = [a_x, a_y, a_z] \) and \( B = [b_x, b_y, b_z] \):

The resulting vector is perpendicular to both A and B, following the right-hand rule.

4. Using the Calculator

Instructions: Enter comma-separated values for both vectors (2 or 3 elements each). The calculator will compute the cross product.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between cross product and dot product?
A: Cross product returns a vector perpendicular to both inputs, while dot product returns a scalar representing their parallel component.

Q2: Can I calculate cross product for 2D vectors?
A: Yes, but it returns a scalar representing the z-coordinate of what would be the 3D cross product.

Q3: What are practical applications of cross product?
A: Used in physics (torque), computer graphics (surface normals), and engineering (moment calculations).

Q4: Why is the result vector perpendicular?
A: This is a fundamental property of the cross product operation in vector mathematics.

Q5: How does numpy.cross() handle non-3D vectors?
A: For 2D vectors, it returns the scalar z-component. For higher dimensions, it's more complex and less commonly used.