Understanding vector cross products is crucial for physics, engineering, and computer graphics. Our calculator not only computes A × B instantly but also shows the step-by-step process—perfect for learning and verification. Enter any two 3D vectors to see the orthogonal result vector and its magnitude, with all intermediate calculations explained.
3D Cross Product Calculator
3D Vector Cross Product Formula
The cross product of two 3D vectors A and B is:
This produces a vector orthogonal to both A and B, with magnitude equal to the area of the parallelogram they span.
How to Use This Cross Product Calculator
1. Enter Vectors
Input components for vectors:
- A = (Ax, Ay, Az)
- B = (Bx, By, Bz)
2. Click “Compute A × B”
- Get the resulting vector (cx, cy, cz)
- See the magnitude ‖A × B‖
- Bonus: Press Enter after typing to calculate instantly
3. Study the Steps
The calculator reveals:
- How each component (X, Y, Z) is derived
- Intermediate multiplications and subtractions
- Magnitude calculation via √(cx² + cy² + cz²)
Also, check more Math Calculators
Cross Product FAQs
What does the cross product result mean?
The result is a vector perpendicular to both input vectors, with magnitude equal to the area of the parallelogram they form.
Why is my cross product zero?
A zero result means your input vectors are parallel (or one is zero). Try (1,2,3) × (2,4,6) to see this.
How is this different from a dot product?
Cross products yield vectors (used for perpendiculars), while dot products yield scalars (used for projections).