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Show that | vec a| vec b+| vec b| vec a ...

Show that `| vec a| vec b+| vec b| vec a` is a perpendicular to `| vec a| vec b-| vec b| vec a ,` for any two non-zero vectors ` vec aa n d vec bdot`

Text Solution

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Case 1 when `veca and vecb` are collinear
=`(|veca|vecb+|vecb|veca|)bot(|veca|vecb-|vecb|veca|)`
=Case 2 when they are not collinear
=`||veca|vecb+|vecb|veca|!=0 (1)`
=`||veca|vecb-|vecb|veca|!=0(2)`
muptiplying equation 1 and 2
=`|veca|^2|vecb|^2-|vecb|^2|veca|^2`
=0
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