If the vectors `veca, vecb, and vecc` are coplanar show that `|(veca,vecb,vecc),(veca.veca, veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc)|=0`

Explanation

To show that if the vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) are coplanar, then

\[ |(\vec{a}, \vec{b}, \vec{c}), (\vec{a} \cdot \vec{a}, \vec{a} \cdot \vec{b}, \vec{a} \cdot \vec{c}), (\vec{b} \cdot \vec{a}, \vec{b} \cdot \vec{b}, \vec{b} \cdot \vec{c})| = 0, \]

we can follow these steps:

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