If `veca and vecb` are non - zero vectors such that `|veca + vecb| = |veca - 2vecb|` then

Options

A. `2 veca. vecb= |vecb|^(2)`
B. ` veca. vecb= |vecb|^(2)`
C. least value of `veca . vecb + 1/(|vecb|^(2) + 2) " is " sqrt2`
D. least value of `veca .vecb + 1/(|vecb|^(2) + 2) " is " sqrt2 -1 `

Answer

a,d

Explanation

` |veca+vecb|= |veca-2vecb|`
`Rightarrow veca.vecb= (|vecb|^(2))/2`
Also `veca.vecb + 1/(|vecb|^(2) +2)`
`(|vecb|^(2)+2)/2+ 1/(|vecb|^(2)+2)-1`
`ge sqrt2-1 `