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Difference between revisions of "Mixed product"

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''<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064240/m0642401.png" /> of vectors <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064240/m0642402.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064240/m0642403.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064240/m0642404.png" />''
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''of vectors $\mathbf{a},\mathbf{b},\mathbf{c}$''
  
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The [[Inner product|inner product]] of the vector <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064240/m0642405.png" /> by the [[Vector product|vector product]] of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064240/m0642406.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064240/m0642407.png" />:
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The [[inner product]] of the vector $\mathbf{a}$ by the [[vector product]] of $\mathbf{b}$ and $\mathbf{c}$:
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$$
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[\mathbf{a},\mathbf{b},\mathbf{c}] = \mathbf{a} \times (\mathbf{b} \cdot \mathbf{c})
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$$
  
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<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m064/m064240/m0642408.png" /></td> </tr></table>
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See [[Vector algebra]].
  
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See [[Vector algebra|Vector algebra]].
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====Comments====
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The phrase '''scalar triple product''' also occurs instead of mixed product.
  
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====Comments====
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{{TEX|done}}
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The phrase scalar triple product also occurs instead of mixed product.
 

Revision as of 08:06, 14 January 2018

of vectors $\mathbf{a},\mathbf{b},\mathbf{c}$

The inner product of the vector $\mathbf{a}$ by the vector product of $\mathbf{b}$ and $\mathbf{c}$: $$ [\mathbf{a},\mathbf{b},\mathbf{c}] = \mathbf{a} \times (\mathbf{b} \cdot \mathbf{c}) $$

See Vector algebra.

Comments

The phrase scalar triple product also occurs instead of mixed product.

How to Cite This Entry:
Mixed product. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Mixed_product&oldid=42730
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