I have a physics problem about vectors:
Two vectors $\boldsymbol{A}$ and $\boldsymbol{B}$ have precisely equal magnitudes. For the magnitude of $\boldsymbol{A} + \boldsymbol{B}$ to be $100$ times larger than the magnitude of $\boldsymbol{A} - \boldsymbol{B}$, what must be the angle between them?
I have tried to draw a diagram and calculate the problem with geometrical methods with two simultaneous equations of the form $c^2 = a^2 + b^2 - 2ab \cos θ$:$$ |\boldsymbol{A} + \boldsymbol{B}|² = |\boldsymbol{A}|² + |\boldsymbol{B}|² - 2|\boldsymbol{A}||\boldsymbol{B}|\cos θ\\ |\boldsymbol{A} - \boldsymbol{B}|² = |\boldsymbol{A}|² + |\boldsymbol{B}|² - 2|\boldsymbol{A}||\boldsymbol{B}|\cos(π - θ) $$ Equating these two equations in terms of $θ$ gives$$ \cos θ = -\frac{9999|\boldsymbol{A} + \boldsymbol{B}|²}{|4|\boldsymbol{A}|²|}. $$
This is as far as i could get, any help solving the problem will be greatly appreciated