Two equal vector have a resultant equal to either of them, then the angle between them will be:

Explanation

Let two vectors are A and B, inclined at an angle `theta`.

Resltant of two vectors A and b
`|R|=sqrt(|A|^(2)+|B|^(2)+2|A||B|costheta)`
Observing `theta=0^(@)`, givens
`|R|=|A|+|B|,"which istrue"`
`Let, |A|=|B|=a`
According to the question , `|R|=a`
From Eq.(i),
`a=sqrt(a^(2)+a^(2)+aa cas theta)`
`implies a^(2)+a^(2)+2a^(2) cas theta `
`implies 2a^(2)cos theta =-a^(2) implies cos theta =- 1//2`
`implies -cos theta =1//2 implies cos theta (180^(@)-theta)=cos 60^(@) `
`implies theta =120^(@)`

Geometrically ,
`/_SOP=120^(@)`