Let \(\vec{a}=2 \hat{i}-\hat{j}+2 \hat{k}\) and \(\vec{b}=\hat{i}+2 \hat{j}-\hat{k}\). Let a vector \(\vec{v}\) be in th…

Let \(\vec{a}=2 \hat{i}-\hat{j}+2 \hat{k}\) and \(\vec{b}=\hat{i}+2 \hat{j}-\hat{k}\). Let a vector \(\vec{v}\) be in the plane containing \(\vec{a}\) and \(\vec{b}\). If \(\vec{v}\) is perpendicular to the vector \(3 \hat{i}+2 \hat{j}-\hat{k}\) and its projection on \(\vec{a}\) is 19 units, then \(|2 \vec{v}|^2\) is equal to__________

[JEE Main 2021, 1 Sep (Shift 2)]