Cross Product Calculator Two Vector

Cross Product Formula:

\[ A × B = (A_yB_z - A_zB_y, A_zB_x - A_xB_z, A_xB_y - A_yB_x) \]

Vector A (x):

Vector A (y):

Vector A (z):

Vector B (x):

Vector B (y):

Vector B (z):

Cross Product Result (A × B):

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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. Its magnitude relates to the area of the parallelogram formed by the two vectors.

2. How Does the Calculator Work?

The calculator uses the cross product formula:

\[ A × B = (A_yB_z - A_zB_y, A_zB_x - A_xB_z, A_xB_y - A_yB_x) \]

Where:

\( A \) — First vector (A_x, A_y, A_z)
\( B \) — Second vector (B_x, B_y, B_z)
\( × \) — Cross product operator

Explanation: The result is a new vector perpendicular to both A and B, following the right-hand rule.

3. Importance of Cross Product

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

4. Using the Calculator

Tips: Enter all six components (x,y,z for both vectors). The calculator will compute the resulting vector components.

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 the magnitude of the cross product represent?
A: It equals the area of the parallelogram formed by the two vectors.

Q3: Can you compute cross product in 2D?
A: Technically no, but you can treat 2D vectors as 3D with z=0, resulting in a vector with only z-component.

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

Q5: When is the cross product zero?
A: When vectors are parallel or one/both are zero vectors.