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प्रश्न
If `veca` and `vecb` are two vectors such that `|veca + vecb| = |vecb|`, then prove that `(veca + 2vecb)` is perpendicular to `veca`.
उत्तर
Given, `|veca + vecb| = |vecb|`
On squaring both sides, we get
`|veca + vecb|^2 = |vecb|^2`
⇒ `|veca|^2 + |vecb|^2 + 2|veca||vecb| = |vecb|^2`
⇒ `|veca|^2 + 2|veca||vecb|` = 0
⇒ `|veca|.(|veca| + 2|vecb|)` = 0
⇒ `veca.(veca + 2vecb)` = 0
Since, dot product of `veca` and `veca + 2vecb` is zero, thus vectors are perpendicular.
Hence proved
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