 Setting "ai" = "ci" and "bj" = "dj", it gives the Lagrange's identity, which is a stronger version of the Cauchy–Schwarz inequality for the Euclidean space formula_2.When , the first and second terms on the right hand side become the squared magnitudes of dot and cross products respectively; in dimensions these become the magnitudes of the dot and wedge products.We may write it

where , , , and are vectors.