1. What is Vector 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 spanned by the two vectors.

2. How Does the Calculator Work?

The calculator uses the standard cross product formula:

Where:

• \( \vec{A} = (A_x, A_y, A_z) \) — First vector
• \( \vec{B} = (B_x, B_y, B_z) \) — Second vector
• \( \hat{i}, \hat{j}, \hat{k} \) — Unit vectors in x, y, z directions

3. Applications of Cross Product

Details: The cross product is used in physics (torque, angular momentum), computer graphics (surface normals), engineering (moment of force), and navigation (great-circle navigation).

4. Using the Calculator

Tips: Enter the x, y, z components of both vectors. The calculator will compute the cross product 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 quantity, while cross product gives a vector quantity perpendicular to both input vectors.

Q2: What does the magnitude of the cross product represent?
A: The magnitude equals the area of the parallelogram formed by the two vectors.

Q3: What happens if vectors are parallel?
A: The cross product will be the zero vector (0, 0, 0).

Q4: Is cross product commutative?
A: No, \( \vec{A} \times \vec{B} = -(\vec{B} \times \vec{A}) \) (anti-commutative).

Q5: Can this be used for 2D vectors?
A: For 2D vectors, treat them as 3D with z=0, and the result will be along the z-axis.