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If bar(c)=3bar(a)-2bar(b), then prove th...

If `bar(c)=3bar(a)-2bar(b)`, then prove that `[bar(a)bar(b)bar(c)]=0`.

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To prove that \([ \bar{a}, \bar{b}, \bar{c} ] = 0\) given that \(\bar{c} = 3\bar{a} - 2\bar{b}\), we will follow these steps: ### Step 1: Substitute \(\bar{c}\) in the scalar triple product We start with the scalar triple product \([ \bar{a}, \bar{b}, \bar{c} ]\). By substituting the expression for \(\bar{c}\), we have: \[ [ \bar{a}, \bar{b}, \bar{c} ] = [ \bar{a}, \bar{b}, 3\bar{a} - 2\bar{b} ] \] ...
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