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Question
Prove that `(veca + vecb).(veca + vecb)` = `|veca|^2 + |vecb|^2` if and only if `veca . vecb` are perpendicular, given `veca != vec0, vecb != vec0.`
Solution
`(veca + vecb) xx (veca + vecb) = |veca|^2 + |vecb|^2`
`veca xx veca + veca xx vecb + vecb xx veca + vecb xx vecb = |veca|^2 + |vecb|^2`
`|veca|^2 + 2veca xx vecb + |b|^2 = |veca|^2 + |vecb|^2`
`2veca xx vecb = 0`
`veca xx vecb = 0`
`veca, vecb` are perpendicular.
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