With the help of the basic notions in differential geometry,such as wedge product,differential form and Hodge star-operator,we explored the geometric nature of the pseudovector is a differential 2-form,and give a reasonable explanation that the differential 2-form can be called pseudovector with the help of Hodge star-operator.The logical relations of pseudovector,true vector and their mixed operation rules are clearly explained by replacing the cross product operation with exterior product operation.And the application of pseudovector and its operation in mechanics and electrodynamics is illustrated with examples.Especially,the reasonable logical explanation that the centripetal acceleration is a true vector is given by applying the operation rules of the pseudovector.
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