There is a formula that if vec c is the resultant of vec a & vec b having an angle between them theta it forms, c^2=a^2+b^2-2abcostheta (a, b, c are the magnitude of vec a,vec b,vec c respectively).
Hence, c^2=a^2+b^2-2abcostheta =>2a²=2a²+2a²costheta =>costheta=0 =>theta=90°.