Returns the cross product \(a \times b\) of two three-dimensional numeric vectors. Provided as an explicit helper because base R has no built-in cross product and inlining it in every consumer obscures the geometry.
Details
By construction \(a \times b\) is orthogonal to both \(a\) and
\(b\); its norm equals \(\|a\|\,\|b\|\,\sin\theta\) where
\(\theta\) is the angle between the inputs (angle_between).
The scalar triple product \(a \cdot (b \times c)\) that appears in
the Van Oosterom-Strackee formula (solid_angle_3d) is the
signed volume of the parallelepiped spanned by \(a, b, c\).
References
Strang, G. (2016). Introduction to Linear Algebra, 5th edition. Wellesley-Cambridge Press. ISBN 978-0980232776.
See also
angle_between for the related angle helper;
solid_angle_3d, spherical_triangle_area
for the consumers in the 3D solid-angle formulas.