Understand the subject
What does a cross product do?
A cross product creates a vector perpendicular to two three-dimensional input vectors. Its length equals the parallelogram area they span.
Use it for oriented area and right-hand-rule normal directions in three dimensions.
The relationship
The defining relationship
u×v=−(v×u); ‖u×v‖=‖u‖‖v‖sin θ
See the structure
What the calculation is doing
input vector× Aoutput vectoru×v=−(v×u); ‖u×v‖=‖u‖‖v‖sin θ
Worked interpretation
Read the result in context
u×v=−(v×u); ‖u×v‖=‖u‖‖v‖sin θ
Interpret with care
Important boundary
It exists in this familiar form only for three-dimensional vectors, and swapping inputs reverses direction.
Use the Matrix Calculator to experiment with small exact matrix operations before applying a more specialized route.