JEE Main 2022 · 28 Jul · Shift 1, Mathematics question 6

Let a vector $\vec a$ has magnitude 9. Let a vector $\vec b$ be such that for every $(x,y)\in\mathbf R\times\mathbf R-\{(0,0)\}$, the vector $\left(x\vec a+y\vec b\right)$ is perpendicular to the vector $\left(6y\vec a-18x\vec b\right)$. Then the value of $\left|\vec a\times\vec b\right|$ is equal to :