If ` veca, vecb` are unit vectors such that ` |veca +vecb|=1 and |veca -vecb|=sqrt3`, " then " |3veca +2vecb|=`A. 7B. 4C. ` sqrt7`D. `sqrt19`

If ` veca, vecb` are unit vectors such that ` |veca +vecb|=1 and |veca

1.	If ` veca, vecb` are unit vectors such that ` \|veca +vecb\|=1 and \|veca -vecb\|=sqrt3`, " then " \|3veca +2vecb\|=`A. 7B. 4C. ` sqrt7`D. `sqrt19`
Answer» Correct Answer - C Let `theta` the angle between `veca and vecb` . Then, ` tan "" theta/2= (\|veca -vecb\|)/(\|veca +vecb\|) Rightarrow tan "" theta/2 = sqrt3 Rightarrow theta =120^(@)` ` veca.vecb = \|veca\|\|vecb\| cos theta =cos 120^(@) = -1/2` Now , ` \|3 veca = 2vecb\|^(2) = 9 \|veca\|^(2) + 4 \|vecb\|^(2) + 12(veca .vecb)` ` Rightarrow \|3veca + 2veca\|^(2) = 9 +4+12 xx ( - 1/2) =7` ` Rightarrow \|3veca +2vecb\|= sqrt7`

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If ` veca, vecb` are unit vectors such that ` |veca +vecb|=1 and |veca -vecb|=sqrt3`, " then " |3veca +2vecb|=`A. 7B. 4C. ` sqrt7`D. `sqrt19`

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