Cross Product Calculator

Calculate the cross product of two 3D vectors quickly and accurately. Enter the x, y, and z components for both vectors to get the resulting perpendicular vector.

Vector A

×

Vector B

Result: A × B

Click calculate to see result

Steps

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Understanding Cross Products in 3D Space

What is a Cross Product?

The cross product of two vectors results in a third vector that is perpendicular to both input vectors. This operation is fundamental in physics, engineering, and computer graphics.

Properties of Cross Products

  • The resulting vector is perpendicular to both input vectors
  • The magnitude depends on both the lengths of the vectors and the angle between them
  • The direction follows the right-hand rule
  • Cross products are anti-commutative: A × B = -(B × A)

Formula and Calculation

For vectors A(ax, ay, az) and B(bx, by, bz), the cross product is:

A × B = (ay·bz - az·by)i - (ax·bz - az·bx)j + (ax·by - ay·bx)k