True or False

Geometry Level 4

State True or False :

Let \(\vec{\color{blue}a} , \vec{\color{red}b} , \vec{\color{purple}c}\) be unit vectors such that \(\vec{\color{blue}a} + \vec{\color{red}b} + \vec{\color{purple}c} = 0\).
Then, \(\vec{\color{blue}a} \times \vec{\color{red}b} \ , \ \vec{\color{red}b} \times \vec{\color{purple}c} \ , \ \vec{\color{purple}c} \times \vec{\color{blue}a}\) are mutually perpendicular.

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