Let \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) represent respectively \(\overrightarrow{BC}\), \(\overrightarrow{CA}\), and \(\overrightarrow{AB}\) where ABC is a triangle. Then,

Question

\(\vec{a} + \vec{b} = \vec{c}\)

\(\vec{b} + \vec{c} = \vec{a}\)

\(\vec{a} \times \vec{b} = \vec{b} \times \vec{c} = \vec{c} \times \vec{a}\)

\([\vec{a} \vec{b} \vec{c}] = [\vec{b} \vec{c} \vec{a}] = [\vec{c} \vec{a} \vec{b}] \neq 0\)

Solution

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