Extended standard vector analysis for plasma physics

Standard vector analysis in three dimensional space is extended by two vector identities that are important for plasma physics applications. A conventional list of vector analytical formulas is examined. Expressions for inverse Delta dot product (alpha a equivalent), inverse Delta x (alpha a equivalent), inverse Delta (alpha a equivalent), inverse Delta dot product (a equivalent x b equivalent), inverse Delta x (a equivalent x b equivalent), inverse Delta (a equivalent dot product b equivalent), and sometimes inverse Delta dot product (a equivalent b equivalent) are given. Cases of higher order differentiation, special coordinate systems, and integral theorems are mentioned. Results complete the list of formulas for two vector fields and one inverse Delta operator. Formulas which involve three vector fields and one inverse Delta operator are introduced. Examples in magnetohydrodynamics and from guiding center drift theories are discussed.