The quantity product,vector product,and mixed product of vectors are important contents of vector algebra and spatial analytic geometry in higher mathematics.This article explores the application of vector mixed product from four aspects:calculating tetrahedral volume,plane equation,line equation,and determining the different faces of two lines.By using multiple solutions to one problem,we broaden our problem—solving ideas,optimize problem—solving methods,enhance students'learning interest,and further improve the teaching effectiveness and quality of higher mathematics.