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Mathematics-Online course: Vector Calculus - Parallelepidial Product

Parallelepidial Product - Calculation of Coordinates


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If the vectors $ \vec{u}$ , $ \vec{v}$ and $ \vec{w}$ span a proper parallelepiped, then every vector $ \vec{x}$ can be represented by a linear combination

$\displaystyle \vec{x} =
\alpha \vec{u} + \beta \vec{v} + \gamma \vec{w}
$

with the coefficients

$\displaystyle \alpha = \frac{[\vec{x},\vec{v},\vec{w}]}
{[\vec{u},\vec{v},\vec...
...
\gamma = \frac{[\vec{x},\vec{u},\vec{v}]}
{[\vec{w},\vec{u},\vec{v}]}\,
.
$


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  automatically generated 10/30/2007