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If vector c = 3a - 2b prove that [a b c] = 0

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We use the results :

\(\overline{b} \times \overline{b} = 0\) and if in a scalar triple product, two vectors are equal, then the scalar triple product is zero.

Alternative Method :

\(\therefore \overline{c}\) is a linear combination of \(\overline{a}\) and \(\overline{b}\)

\(\therefore\) \(\overline{a}\)\(\overline{b}\)\(\overline{c}\) are coplanar

\(\therefore\) [\(\overline{a}\) \(\overline{b}\) \(\overline{c}\)] = 0.

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