Einstein Summation Convention || Triple Product Vectors || Alternating Tensor || Vector Algebra

Product of Three Vectors

The triple product of three vectors A, B and C which will be explained are those of the form A.(B cross C) and A cross B cross C. other triple product such as (A.B)C etc.

A.(B cross C) is called the Scalar triple product  and A cross B cross C is called Vector Triple Product.

Einstein Summation Convention
Triple Product of Vectors

we may even write A. B cross C having bracket between B and C with understanding that the cross product is between B and C first.

Vector product using Alternating Tensor  we define using a Special Symbol.

scalar triple product and vector triple product
Alternating Tensor and Product of Three Vectors
According to the Summation Convention, when an index variable appears twice in a single term and it implies summation of that term over all the values of the index.

tensor numericals
Einstein Summation Convention