If $ \vec{a} $, $ \vec{b} $, and $ \vec{c} $ are three vectors such that $ \vec{a} + \vec{b} + \vec{c} = \vec{0} $, then which of the following is true?

Question

$ \vec{a} \cdot \vec{b} = \vec{b} \cdot \vec{c} = \vec{c} \cdot \vec{a} $

$ \vec{a} \times \vec{b} = \vec{b} \times \vec{c} = \vec{c} \times \vec{a} $

$ \vec{a} \times \vec{b} = \vec{b} \times \vec{a} = \vec{c} \times \vec{b} $

$ \vec{b} \times \vec{a} = \vec{b} \times \vec{c} = \vec{c} \times \vec{a} $

Solution

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