Definition:Vector Triple Product

Definition

Let $\mathbf a$, $\mathbf b$ and $\mathbf c$ be vectors in a Cartesian $3$-space:

$\ds \mathbf a$

$=$

$\ds a_i \mathbf i + a_j \mathbf j + a_k \mathbf k$

$\ds \mathbf b$

$=$

$\ds b_i \mathbf i + b_j \mathbf j + b_k \mathbf k$

$\ds \mathbf c$

$=$

$\ds c_i \mathbf i + c_j \mathbf j + c_k \mathbf k$

where $\tuple {\mathbf i, \mathbf j, \mathbf k}$ is the standard ordered basis of $\mathbf V$.

The vector triple product is defined as:

$\mathbf a \times \paren {\mathbf b \times \mathbf c}$

where $\times$ denotes the vector cross product.

The vector triple product is also known as the triple vector product.

Some sources use the term repeated cross product.