यदि |a|=7, |b|=11 और |a+b|=`10sqrt3` तो `|a-b|` किसके बारहर है

Options

A. 40
B. 10
C. `4sqrt10`
D. `2sqrt10`

Answer

D

Explanation

दिया है `|a|=7,|b|=11`
तथा `|a+b|=10sqrt3`
हम जानते है की `|a+b|^(2)=(a+b).(a+b)`
`|a+b|^(2)=(a+b).(a+b)`
`Rightarrow (10sqrt3)^(2)`
`=a.a+a.a+b.a+b.b`
`Rightarrow a.a+a.a+b.a+b.b`
अब `Rightarrow |a-b|^(2)=(a-b).(a-b)`
`Rightarrow 300=49+2(a.b)+121`
`Rightarrow 2(a.b)=300-170=130`
`Rightarrow (a.b)=65`
`|a-b|^(2)=(a-b).(a-b)`
`=|a|^(2)-2(a.b)+|b|^(2)`
`=49-130+121`
`=170-130=40`
`=|a-b|=sqrt40`
`=|a-b|=sqrt40`
`=2sqrt10`