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

Explanation

Let `p=|a|b+|b|` is a perpendicular to `|a|b-|b|a`
Then `p.q =(|a|b+|b|a).(|a|b-|b|a)`
`=|a|^2(b.b)-|a||b|(b.a)+|b| |a|(a.b)-|b|^2(a.a)`
`=|a|^2|b|^2-|a| |b| (a.b)+|a||b|(a.b)-|b|^2 |a|^2=0`.
`rArr p bot q ( because If c.d =0 rArr c " is perpnedicular tod ")`
Hence , `|a|b+|b|a and |a| b-|b|` a are perpendicular to each other for any two non -zero vectors a and b.