the.com/cross product
Two vectors walk into a plane; a third walks out perpendicular to both.
means A way of multiplying two vectors in 3D space that produces a new vector perpendicular to both of the originals, with a length equal to the area of the parallelogram they form.
from The name is refreshingly literal: 'cross' from the X-shaped multiplication symbol (×) early mathematicians used to write it, as opposed to the dot product's '·'. The notation and concept were developed in the 1800s, growing out of work by Hamilton on quaternions and refined by Gibbs and Heaviside, who split the quaternion machinery into the separate dot and cross products vector algebra still uses today.
- result type
- a vector, not a scalar, unlike its dot cousin
- magnitude meaning
- equals area of the parallelogram they span
- order matters
- swap vectors, flip the direction, a times b equals negative b times a
- zero case
- vanishes when vectors are parallel, nothing to span