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Question

Using properties of scalar triple product, prove that [¯¯¯a+¯¯b¯¯b+¯¯c¯¯c+¯¯¯a]=2[¯¯¯a¯¯b¯¯c].

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Solution

We have to prove that
[¯¯¯a+¯¯b¯¯b+¯¯c¯¯c+¯¯¯a]=2[¯¯¯a¯¯b¯¯c](¯¯¯a+¯¯b).((¯¯b+¯¯c)(¯¯c+¯¯¯a))(¯¯¯a+¯¯b).(¯¯bׯ¯c+¯¯bׯ¯¯a+¯¯cׯ¯¯a)[¯¯¯a¯¯b¯¯c]+[¯¯¯a¯¯b¯¯c]=2[¯¯¯a¯¯b¯¯c]
Hence, proved.


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