Final answer:
The statement 'u03b71∧η2∧η3 is exact' is FALSE because in ℝ³, a three-form cannot be the exterior derivative of a higher degree form as four-forms do not exist in three-dimensional space.
Step-by-step explanation:
The question asks to justify whether the exterior product of any three one-forms η1, η2, η3 in ℝ³ (the three-dimensional real number space) is exact. A differential form is considered exact if it is the exterior derivative of another differential form. In ℝ³, a three-form is the highest-degree form possible, which means that it cannot be the exterior derivative of a four-form, because four-forms do not exist in three-dimensional space. Therefore, the statement 'η1∧η2∧η3 is exact' is FALSE. This is a consequence of the property that the exterior derivative increases the degree of a differential form by one, and since there can't be a form of a higher degree than three in ℝ³, the given three-form can't be exact.