Category:Scalar Triple Product

This category contains results about Scalar Triple Product.
Definitions specific to this category can be found in Definitions/Scalar Triple Product.

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 scalar triple product of $\mathbf a$, $\mathbf b$ and $\mathbf c$ is defined and denoted as:

$\sqbrk {\mathbf a, \mathbf b, \mathbf c} := \mathbf a \cdot \paren {\mathbf b \times \mathbf c}$

where:

$\cdot$ denotes dot product

The scalar triple product of $\mathbf a$, $\mathbf b$ and $\mathbf c$ is defined and denoted as:

$\sqbrk {\mathbf a, \mathbf b, \mathbf c} := \begin {vmatrix} a_i & a_j & a_k \\ b_i & b_j & b_k \\ c_i & c_j & c_k \\ \end {vmatrix}$

where $\begin {vmatrix} \ldots \end {vmatrix}$ is interpreted as a determinant.

Pages in category "Scalar Triple Product"

The following 6 pages are in this category, out of 6 total.