# Vector cross product calculator

# Vector cross product

The vector cross product, also known as the vector product or cross product, is an operation performed on two vectors in three-dimensional space that results in a new vector that is perpendicular to both of the original vectors. The cross-product is defined as:

A × B = |A| |B| sin(θ) n

**where:**

**A and B are the two vectors being multiplied****|A| and |B| are the magnitudes of A and B, respectively****θ is the angle between A and B, measured in radians****n is a unit vector perpendicular to both A and B in the direction determined by the right-hand rule**

The right-hand rule states that if you point your right thumb in the direction of A and your right index finger in the direction of B, the vector product will point in the direction of your middle finger.

**The magnitude of the cross product is given by:**

|A × B| = |A| |B| sin(θ)

**To calculate the components of the cross product vector, you can use the following determinant:**

A × B = | i j k |

| Ax Ay Az |

| Bx By Bz |

where i, j, and k are the unit vectors in the x, y, and z directions, respectively, and Ax, Ay, Az, Bx, By, and Bz are the components of vectors A and B.

**The resulting vector will have components (Cx, Cy, Cz) given by:**

**Cx = AyBz – AzBy**

**Cy = AzBx – AxBz**

**Cz = AxBy – AyBx**

The vector cross product is used in various applications, including physics, engineering, and computer graphics, to calculate torque, angular momentum, and the normal vector to a plane, among other things.