Cross Product Calculator
Calculate the cross product of two 3D vectors.
Inputs
Three comma-separated values
Three comma-separated values
Magnitude
7.348469
X Component
-3.000000
Y Component
6.000000
Z Component
-3.000000
Step by step
x component: a_y×b_z − a_z×b_y
2×6 − 3×5
= -3.000000
y component: a_z×b_x − a_x×b_z
3×4 − 1×6
= 6.000000
z component: a_x×b_y − a_y×b_x
1×5 − 2×4
= -3.000000
Magnitude
√(-3.00² + 6.00² + -3.00²)
= 7.348469
How it works
The cross product of two 3D vectors produces a third vector perpendicular to both, with magnitude equal to the area of the parallelogram they span. It is used in computer graphics, physics simulations, and 3D geometry calculations within ML pipelines.
Formula
Cross Product
a × b = (a_y*b_z - a_z*b_y, a_z*b_x - a_x*b_z, a_x*b_y - a_y*b_x)
- a, b
- 3-dimensional input vectors
Frequently Asked Questions
Why is the cross product only defined in 3D?
The cross product as a vector operation is specific to 3D (and 7D) because it relies on the structure of the space to produce a unique perpendicular vector. In other dimensions, the wedge product generalizes this concept.
How is the cross product used in ML?
It is used in 3D point cloud processing, computer vision for surface normal estimation, robotics, and any ML application involving 3D geometric reasoning.