Cross Product Calculator

Calculate the cross product of vectors in any dimension instantly. Supports 2D, 3D, and higher-dimensional vectors with flexible input using commas or spaces.

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Understanding Cross Products

The cross product is a binary operation on two vectors in three-dimensional space that results in a vector perpendicular to both input vectors. This mathematical operation is essential in physics, engineering, computer graphics, and many other fields.

How to Use This Calculator

  1. Enter the X, Y, and Z components of your first vector (Vector A)
  2. Enter the X, Y, and Z components of your second vector (Vector B)
  3. Click "Compute Cross Product" to see the result
  4. The calculator will display both the resulting vector and its magnitude

Applications of Cross Products

  • Physics: Calculating torque, angular momentum, and magnetic force
  • Computer Graphics: Computing surface normals for lighting calculations
  • Engineering: Analyzing forces and moments in mechanical systems
  • Mathematics: Finding areas of parallelograms and solving geometric problems

Mathematical Properties

The cross product has several important properties that make it useful in various applications:

  • The result is always perpendicular to both input vectors
  • The magnitude equals the area of the parallelogram formed by the two vectors
  • The direction follows the right-hand rule
  • If vectors are parallel, the cross product is zero