Vector A and vector B are two vectors such that their resultant is perpendicular to vector A and in magnitude equal to A .Find the magnitude of vector B ?

According to question vector a perpendicular to vector a + b and modulus of vector a equals to a + b therefore vector a A + B and b vector forms right angle isoscales Triangle and b vector is hypotenuse of triangle therefore modulus of b vector = under root 2 mode of vector a