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Question

If ¯c=¯3a¯2b, then prove that [¯a¯b¯c]=0

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Solution

Given that,
¯¯c=3¯¯¯a2¯¯b
To prove;[¯¯¯a¯¯b¯¯c]=0
¯¯bׯ¯b=0
In a scalar triple product , two vector are equal then the scalar triple product is Zero.
L.H.S=
=[¯¯¯a¯¯b¯¯c]=¯¯¯a(¯¯b×(3¯¯¯a2¯¯b))=¯¯¯a(3¯¯¯aׯ¯b2¯¯bׯ¯b)=¯¯¯a(3¯¯¯aׯ¯b0)=3¯¯¯aׯ¯¯aׯ¯b=0ׯ¯b
=0 R.H.S
Proved.

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