Two vectors, both equal in magnitude, …

|A+B−→−−−|=|A→|2+|B→|2+2|A→||B→|cosθ−−−−−−−−−−−−−−−−−−−−−−−√ Complete answer: Let the two vectors be |A→| and |B→|. θ be the angle between both the vectors. Both the vectors have the same magnitude. ∴|A→|=|A→| …(1) Let the resultant have magnitude equal to vector A. Thus, the resultant is given by, |A→|=|B→|=|A+B−→−−−| …(2) The magnitude of resultant of two vectors is given by, |A+B−→−−−|=|A→|2+|B→|2+2|A→||B→|cosθ−−−−−−−−−−−−−−−−−−−−−−−√ …(3) From the equation. (2) and equation. (3) we get, |A→|=|A→|2+|B→|2+2|A→||B→|cosθ−−−−−−−−−−−−−−−−−−−−−−−√ Squaring both the sides we get, ⇒|A→|2=|A→|2+|B→|2+2|A→||B→|cosθ Substituting equation. (1) in above equation we get, |A→|2=|A→|2+|A→|2+2|A→||A→|cosθ ⇒|A→|2=2|A→|2+2|A→||A→|cosθ ⇒−|A→|2=2|A→||A→|cosθ ⇒cosθ=−12 ⇒θ=cos−1(12) ⇒θ=120° Hence, the angle between the two vectors is 120°.