Final answer:
The given equation represents the components of the cross product of vectors A and B, as it reflects the sum of products of A's and B's components in accordance with the Levi-Civita symbol and the anticommutative property.
Step-by-step explanation:
To verify that the equation Ci = εijkAjBk = (A × B)i represents the components of the cross product of two vectors A and B, we need to look at the individual scalar components of the cross product.
The cross product A × B can be written as (AyBz - AzBy)Î + (AzBx - AxBz)Ĵ + (AxBy - AyBx)Ê. This formula can be derived by using the anticommutative property, the distributive property, and the specific cross products of the unit vectors î, ĵ, and â.
Thus, the given equation indeed represents the cross product when you evaluate the Levi-Civita symbol εijk and the components of vectors A and B appropriately. It indicates that the scalar component Ci is obtained by summing the products of the other two components of A and B, following both the signs determined by the Levi-Civita symbol and the anticommutative nature of the cross product.