Question: A patent attorney is reviewing a software algorithm that maps user behavior on a 2D grid, where each user’s activity is represented as a vector $\mathbfv = \beginpmatrix a \\ b \endpmatrix$. For the system to ensure fairness, the algorithm must always preserve orthogonality: if $\mathbfv \cdot \beginpmatrix 3 \\ -4 \endpmatrix = 0$, then it must also imply $\mathbfv \cdot \beginpmatrix x \\ y \endpmatrix = 0$ for some integer vector $\beginpmatrix x \\ y \endpmatrix$. What must be true about all such vectors $\mathbfv$? - Abu Waleed Tea