"University calculus"-chape10-vector and spatial geometry-cross product

Introduction of the concept of cross-product:

In order to measure the tilt state of a straight line in the plane, we introduce the concept of inclined angle. By establishing tanα= K in a Cartesian coordinate system, we realize the connection between geometric relations and algebraic relationships, which in fact is a core of solving geometrical problems with computers, and the computer is doing numerical operations, so what you need to do is to express the relations in algebraic relation. In space, in order to indicate the degree of inclination of a plane relative to the spatial Cartesian coordinate system, we measure it by a normal vector of the plane perpendicular to it (as this translates into a problem that describes the degree of linear tilt).

Definition of cross product:

Note that the θ here is based on the order of the right-hand rule and the cross-multiplication, which has a certain directivity, which directly leads to the wide application of the fork multiplication in the computational geometry problem.

Through this definition, we can easily get the following operation law.

Obviously this definition we do not like, because it is still too low in algebra, mainly because the sine of the angle is not easy to find, but this does not affect the definition of the importance of the application, the following problem we need to solve is to find an equivalent algebraic degree of a higher definition.

Determinant formula for cross-product (take two dimensions as an example):

"University calculus"-chape10-vector and spatial geometry-cross product