Vector Algebra: JEE Main 2021 Mathematics question

Let $\overrightarrow a = 2\widehat i - \widehat j + 2\widehat k$ and $\overrightarrow b = \widehat i + 2\widehat j - \widehat k$. Let a vector $\overrightarrow v$ be in the plane containing $\overrightarrow a$ and $\overrightarrow b$. If $\overrightarrow v$ is perpendicular to the vector $3\widehat i + 2\widehat j - \widehat k$ and its projection on $\overrightarrow a$ is 19 units, then ${\left| {2\overrightarrow v } \right|^2}$ is equal to _____________.