ベクトルの公式

$\displaystyle \boldsymbol{A}\cdot\boldsymbol{B}$	$\displaystyle =$	$\displaystyle \boldsymbol{B}\cdot\boldsymbol{C}$	(729)
$\displaystyle \boldsymbol{A}\times\boldsymbol{B}$	$\displaystyle =$	$\displaystyle -\boldsymbol{B}\times\boldsymbol{C}$	(730)
$\displaystyle \boldsymbol{A}\cdot(\boldsymbol{B}\times\boldsymbol{C})$	$\displaystyle =$	$\displaystyle \boldsymbol{B}\cdot(\boldsymbol{C}\times\boldsymbol{A}) =\boldsymbol{C}\cdot(\boldsymbol{A}\times\boldsymbol{B})$	(731)
$\displaystyle \boldsymbol{A}\times(\boldsymbol{B}\times\boldsymbol{C})$	$\displaystyle =$	$\displaystyle (\boldsymbol{A}\cdot\boldsymbol{C})\boldsymbol{B}-(\boldsymbol{A}\cdot\boldsymbol{B})\boldsymbol{C}$	(732)

$\displaystyle \mathop\emph{\text{grad}}\nolimits (fg)$	$\displaystyle =$	$\displaystyle f\mathop\emph{\text{grad}}\nolimits g+g\mathop\emph{\text{grad}}\nolimits f$	(733)
$\displaystyle \mathop\emph{\text{div}}\nolimits (f\boldsymbol{A})$	$\displaystyle =$	$\displaystyle \boldsymbol{A}\mathop\emph{\text{grad}}\nolimits f+f\mathop\emph{\text{div}}\nolimits \boldsymbol{A}$	(734)
$\displaystyle \mathop\emph{\text{rot}}\nolimits (f\boldsymbol{A})$	$\displaystyle =$	$\displaystyle f\mathop\emph{\text{rot}}\nolimits \boldsymbol{A}+\mathop\emph{\text{grad}}\nolimits f\times\boldsymbol{A}$	(735)
$\displaystyle \mathop\emph{\text{grad}}\nolimits (\boldsymbol{A}\cdot\boldsymbol{B})$	$\displaystyle =$	$\displaystyle (\boldsymbol{B}\cdot\mathop{\emph ▽}\nolimits )\boldsymbol{A} +(\boldsymbol{A}\cdot\mathop{\emph ▽}\nolimits )\boldsymbol{B}$
		$\displaystyle +\boldsymbol{A}\times\mathop\emph{\text{rot}}\nolimits \boldsymbol{B}+\boldsymbol{B}\times\mathop\emph{\text{rot}}\nolimits \boldsymbol{A}$	(736)
$\displaystyle \mathop\emph{\text{div}}\nolimits (\boldsymbol{A}\times\boldsymbol{B})$	$\displaystyle =$	$\displaystyle \boldsymbol{B}\mathop\emph{\text{rot}}\nolimits \boldsymbol{A}-\boldsymbol{A}\mathop\emph{\text{rot}}\nolimits \boldsymbol{B}$	(737)
$\displaystyle \mathop\emph{\text{rot}}\nolimits (\boldsymbol{A}\times\boldsymbol{B})$	$\displaystyle =$	$\displaystyle \boldsymbol{A}\mathop\emph{\text{div}}\nolimits \boldsymbol{B}-\boldsymbol{B}\mathop\emph{\text{div}}\nolimits \boldsymbol{A}$
		$\displaystyle +(\boldsymbol{B}\cdot\mathop{\emph ▽}\nolimits )\boldsymbol{A}-(\boldsymbol{A}\cdot\mathop{\emph ▽}\nolimits )\boldsymbol{B}$	(738)

$\displaystyle \mathop\emph{\text{div}}\nolimits (\mathop\emph{\text{grad}}\nolimits f)$	$\displaystyle =$	$\displaystyle \mathop{\emph ▽}\nolimits ^2f$	(739)
$\displaystyle \mathop\emph{\text{rot}}\nolimits (\mathop\emph{\text{grad}}\nolimits f)$	$\displaystyle =$	$\displaystyle \boldsymbol{0}$	(740)
$\displaystyle \mathop\emph{\text{grad}}\nolimits (\mathop\emph{\text{div}}\nolimits \boldsymbol{A})$	$\displaystyle =$	$\displaystyle \mathop\emph{\text{rot}}\nolimits (\mathop\emph{\text{rot}}\nolimits \boldsymbol{A})+\mathop{\emph ▽}\nolimits ^2\boldsymbol{A}$	(741)
$\displaystyle \mathop\emph{\text{div}}\nolimits (\mathop\emph{\text{rot}}\nolimits \boldsymbol{A})$	$\displaystyle =$	0	(742)
$\displaystyle \mathop\emph{\text{rot}}\nolimits (\mathop\emph{\text{rot}}\nolimits \boldsymbol{A})$	$\displaystyle =$	$\displaystyle \mathop\emph{\text{grad}}\nolimits (\mathop\emph{\text{div}}\nolimits \boldsymbol{A})-\mathop{\emph ▽}\nolimits ^2\boldsymbol{A}$	(743)