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If vec aa n d vec b are any two unit ve...

If ` vec aa n d vec b` are any two unit vectors, then find the greatest positive integer in the range of `(3| vec a+ vec b|)/2+2| vec a- vec b|` .

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The correct Answer is:
5
Let angle between `veca and vecb br theta`
we have ` |veca| = |vecb|=1`
Now `|veca + vecb|= 2cos theta/2 and |veca - vecb|=2 sin theta/2`
consider `F(theta) = 3 cos theta/2 + 4 sin theta/2 theta in [ 0,pi]`
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