Let a vector a has magnitude 9. Let a vector b be such that for every (x, y) ∈ R × R -{(0,0)}, the vector (x a +y b ) is perpendicular to the vector…

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