The relationship and application of vector triple product and tetrahedron volume formula
In analytical geometry,the traditional method to calculate the volume of a tetrahedron is to select one vertex as the origin and use three non-coplanar vectors originating from this vertex to obtainthe volume of the tetrahedron by calculating their scalar triple product.However,in reality,it is sufficient to choose any three non-collinear vectors from the four vertices and calculate their scalar triple product to determine the volume of the tetrahedron.This paper proposes a more general method that utilizes the vector triple product to calculate the volume of a tetrahedron and proves its accuracy.Finally,it adopts a numerical example to demonstrate the simplicity and effectiveness.
万方数据
维普
