The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B, The angle between A and B is

Here (A+B)⋅A=0A2+ABcos⁡θ=0or ABcos⁡θ=−A2....(1)Bcos⁡θ=−A...(2)Further, |A+B|=12|B|or (A+B)⋅(A+B)=12|B|2A2+B2+2ABcos⁡θ=14B2or A2+ABcos⁡θ+B2+ABcos⁡θ=14B20+B2+ABcos⁡θ=−14B2or ABcos⁡θ=−34B2 …(3)From eqs. (1) and (3)A2=34B2 or A=(3/2)BFrom eq. (2), Bcos⁡θ=−(3/2)Bor cos⁡θ=−3/2 or θ=150∘