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°#.