Compute the oriented vector perpendicular to two 3D vectors. The page traces how the inputs become cross product before rounding.
It finds normals, torque, angular momentum, orientation, and surface area.
The 3D cross product a×b is perpendicular to both inputs and has magnitude equal to their parallelogram area. Cross Product can be compared with oriented volume.
Preserve the setup beside the output so a later reader can distinguish this calculation from a similar-looking one.
(1,2,3)×(4,5,6)=(−3,6,−3). This Cross Product example can be compared with perpendicularity check.
Order matters: b×a=−(a×b), and this page requires exactly three components.
Changing only one field helps distinguish a data-entry problem from the intended behavior of cross product.
Use the oriented component expansion and verify both dot products with the result are zero.
Transfer the source entries one at a time under vector a and vector b, keeping any units visible in your notes. This page can validate numerical ranges, but only the reader can confirm that each entry represents the intended quantity.
Parallel vectors produce the zero vector. Trying a nearby input should follow this pattern; otherwise inspect the field assignment.
The scalar triple product dots a third vector with this cross product. That neighboring measure needs its own setup rather than a relabeled answer.
Attach units and the name cross product whenever the answer leaves this page. A rounded value is suitable for presentation, while retained working digits are safer for a dependent calculation.
Copying only the decimal discards the setup. Pair the cross product with vector a and vector b and the unit convention so another reader can reconstruct its meaning.
To repeat Cross Product, retain Vector a, and Vector b. Dot the cross product with each original vector. Both results should be zero, and reversing the vector order should reverse the direction.
For Cross Product, attach the chosen coordinate basis because the same components mean something else in another basis.
The 3D cross product a×b is perpendicular to both inputs and has magnitude equal to their parallelogram area.
It finds normals, torque, angular momentum, orientation, and surface area.
Order matters: b×a=−(a×b), and this page requires exactly three components.
Use the oriented component expansion and verify both dot products with the result are zero.