Plane Vector Cross Product Calculator

What is a Plane Vector Cross Product Calculator?

A Plane Vector Cross Product Calculator is a tool that computes the cross product of two vectors in three-dimensional space. The cross product of two vectors results in a third vector that is perpendicular to both input vectors.

Why Use a Plane Vector Cross Product Calculator?

• To find a perpendicular vector to two given vectors.
• To determine the normal vector of a plane.
• To compute torque, angular momentum, or force in physics and engineering.
• To simplify complex 3D vector calculations.

How Does the Calculator Work?

1. Input Two Vectors
   Let vectors A and B be:
   A=(Ax,Ay,Az)
   B=(Bx,By,Bz)
2. Compute the Cross Product
   The cross product formula is:
   
   Expanding the determinant:
   
   Resulting in the vector:
   

When to Use It?

• In physics problems involving rotational forces.
• In 3D computer graphics for lighting and shading.
• In engineering to determine perpendicular forces or directions.
• In robotics for orientation and motion planning.