Abstract: The invariable form of vector-differential operator △↓ in gradient,divergence,rotation and Laplace operator of various orthogonal coordinate systems with differential geometries is studied,and the origin of confusions appeared in the operator △↓ used is also discussed.The opinion and solution of vector operation priority in bracket are advanced,which will remove some misconceptions in the operator △↓.

Key words: vector-differential operator△↓, vector analysis, differential geometry, orthogonal coordinate system