Question

Problem 8.3.8. Show, by referring to Eqn. (8.3.14) that the "box" product of three vectors can be written as a determinant or scalar triple (83.16) By invoking the invariance of the determinant under cyclic change of rows show that the box or scalar triple product is invariant under the cyclic exchange of the three vectors. The antisymmetry of the determinant (i.e., its change of sign under exchange of rows corresponds to the antisymmetry of the cross product of two vectors under the exchange. The vanishing of the determinant when two ro proportional corresponds to the vanishing of the "box" when two of the adjacent edges become parallel. ws are (8.3.14)

Answer 1

"Here A = A_x i^^+ A_y j^^+ A_z k^^, B = B_x i^^+ B_y j^^+ B_z k^^, C = C_x i^^+ C_y j^^+ C_z k^^ Now B times C =