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If veca and vecb are unit vectors, then ...

If `veca and vecb` are unit vectors, then find the greatest value of `|veca+vecb|+ |veca-vecb|` .

Text Solution

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Let `theta` be an angle between unit vectors `veca +vecb`. Then
`veca.vecb= cos theta `
`|veca+ vecb|^(2)=|veca|^(2)+|vecb|^(2)+2veca.vecb`
`2 + cos theta= 4 cos^(2)theta//2`
`or |veca -vecb| = 2cos(theta/2)`
similarly, `|veca-vecb|= 2 sin (theta/2)`
` Rightarrow |veca + vecb|+ |veca -vecb|=2 (cos (theta/2)+sin (theta/2))le2 sqrt2`
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