The three vectors OA,OB,OC have the same magnitude r,then the sum of these vectors have magnitude?

Then angle between vector OB and OA will be 90° now break vector OC into its rectangular components..

Like vector OCcos45° along vector OA and OAsin45° along vector OB then add them simple algebraically where |OA|=|OB|=|OC|=R such as

R+Rcos45° along vector OA

(1+1/√2)R

And

R +Rsin45° along vector OB

(1+1/√2)R

Now apply formula resultant =(A^2 + B^2 + 2ABcos$)^(1/2) where $ is angle between them

Here $ = 90°

So we have sum =(√2 +1)R