If `veca, vecb and vecc` are unit vectors satisfying `|veca-vecb|^(2)+|vecb-vecc|^(2)+|vecc-veca|^(2)=9 " then find the value of " |2veca+ 5vecb+ 5vecc|` .

Answer

3

Explanation

As `|veca-vecb|^(2)+|vecb-vecc|^(2)+|vecc-veca|^(2)`
`=3(|veca|^(2)+|vecb|^(2)+|vecc|^(2))-|veca+vecb+vecc|^(2)`
`Rightarrow 3xx 3-|veca+vecb+vecc|=9`
`or |veca +vecb+vecc|=0`
`veca +vecb +vecc=0`
`or vecb +vecc=-veca`
`Rightarrow |2veca+5(vecb +vecc)|=|-3veca|=3|veca|=3`