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description: 🚧 under construction
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# 純量三重積

[線性代數](../../..) ⟩ [向量](../..) ⟩ [運算](..) ⟩ [三重積]() ⟩ 純量

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( :star: <mark style="color:red;">**只**</mark>適用於<mark style="color:yellow;">**座標空間**</mark>:exclamation:)

$$(\mathbf{u}\times\mathbf{v})\cdot\mathbf{w} = \begin{vmatrix}   u_1 & u_2 & u_3 \\   v_1 & v_2 & v_3 \\   w_1 & w_2 & w_3 \\ \end{vmatrix}$$

:u6307: 同義詞："<mark style="color:purple;">**scalar triple product**</mark>"
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{% tab title="🔸 性質" %}
1. $$(\mathbf{u}\times\mathbf{v})\cdot\mathbf{w} = \mathbf{u}\cdot(\mathbf{v}\times\mathbf{w})$$
2. $$(\mathbf{u}\times\mathbf{v})\cdot\mathbf{w} = (\mathbf{v}\times\mathbf{w})\cdot\mathbf{u}$$ (可由 <mark style="color:yellow;">**1.**</mark> 與[內積交換律](broken-reference)推得)
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{% tab title="📘 手冊" %}
* wiki ⟩ [triple product](https://en.wikipedia.org/wiki/Triple_product)
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{% endtabs %}
