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If |veca+vecb|=|veca-vecb| show that vec...

If `|veca+vecb|=|veca-vecb|` show that `veca_|_vecb`.

Text Solution

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We have `|veca+vecb|^2=(veca+vecb).(veca+vecb)`
`=veca.veca+veca.vecb+vecb.veca+vecb.vecb`
`=a^2+b^2+2veca.vecb`
Similarly
`|veca-vecb|^2=(veca-vecb).(veca.vecb)`
`=a^2+b^2-2veca.vecb`
If `|veca+vecb|=|veca-vecb|`,
`veca^2+vecb^2+2veca.vecb=a^2+b^2-2veca.vecb`
or, `veca.vecb=0`
or, `veca_|_vecb`.
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