Category:Vector Cross Product of Vector Cross Products

Let $\mathbf a, \mathbf b, \mathbf c, \mathbf d$ be vectors in a vector space $\mathbf V$ of $3$ dimensions:

Let $\mathbf a \times \mathbf b$ denote the vector cross product of $\mathbf a$ with $\mathbf b$.

Let $\sqbrk {\mathbf a, \mathbf b, \mathbf c}$ denote the scalar triple product of $\mathbf a$, $\mathbf b$ and $\mathbf c$.

Then:

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

$=$

$\ds \sqbrk {\mathbf a, \mathbf b, \mathbf d} \mathbf c - \sqbrk {\mathbf a, \mathbf b, \mathbf c} \mathbf d$

$\ds $

$=$

$\ds \sqbrk {\mathbf a, \mathbf c, \mathbf d} \mathbf b - \sqbrk {\mathbf b, \mathbf c, \mathbf d} \mathbf a$

Pages in category "Vector Cross Product of Vector Cross Products"

The following 2 pages are in this category, out of 2 total.