Don’t waste your time on the title. You will be given two vectors `$ \vec{v_{1}} = x_{1} \hat{i} + y_{1} \hat{j} $`

and `$ \vec{v_{2}} = x_{2} \hat{i} + y_{2} \hat{j} $`

. Let `$\vec{v_{1}}$`

and `$\vec{v_{2}}$`

form angles `$\theta_{1}$`

and `$\theta_{2}$`

with the positive `$x$`

- axis respectively. Note that the magnitude of `$x_{i} \hat{i} + y_{i} \hat{j}$`

is defined by `$\sqrt{x_{i}^2 + y_{i}^2}$`

.

This is a companion discussion topic for the original entry at https://toph.co/p/1-march-2023