MATH 20C Lecture 6

Geometry of the cross product

Fact: Let be the parallelogram spanned by and
Area of
Area of
Volume of parallelepiped spanned by : (order does not matter)

12.5 Planes in

Plane

A plane is an infinite, flat surface (2D).
an arbitrary point on
normal vector, perpendicular to all lines/vectors parallel to the plane
Note where (scalar form of an equation of the plane)
, unique up to a common scaling of