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Show that |veca|vecb+|vecb|veca is perpe...

Show that `|veca|vecb+|vecb|veca` is perpendicular to `|veca|vecb-|vecb|veca` for any two non zero vectors `veca and vecb.

Text Solution

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`(|veca|vecb+ |vecb|veca).(|veca|vecb- |vecb|veca)`
=`|veca|^(2)vecb.vecb- |veca||vecb|^(2)vecb.veca`
`+ |vecb||veca|veca.vecb-|veca||vecb|^(2)veca.veca`
`= |veca|^(2)|vecb|^(2)-|vecb|^(2)|veca|^(2)`
=0
Hence, `|veca|vecb + |vecb|veca and |veca|vecb- |vecb|veca` are perpendicular to each other .
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