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Let $\vec{a}, \vec{b}, \vec{c}$ be the position vectors of points $A, B, C$ respectively. Under which one of the following conditions are the points $A, B, C$ collinear?
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The correct answer is:
$(\vec{a} \times \vec{b})+(\vec{b} \times \vec{c})+(\vec{c} \times \vec{a})=\overrightarrow{0}$
Points A, B and $\mathrm{C}$ are collinear, if
$(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}})+(\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}})+(\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}})=\overrightarrow{0}$
$(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}})+(\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}})+(\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}})=\overrightarrow{0}$
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