Let \(\vec{a}=2\hat{i}−\hat{j}−\hat{k},\vec{b}=\hat{i}+3\hat{j}−\hat{k}\) and \(\vec{c}=2\hat{i}+\hat{j}+3\hat{k}\). Let…

Let \(\vec{a}=2\hat{i}−\hat{j}−\hat{k},\vec{b}=\hat{i}+3\hat{j}−\hat{k}\) and \(\vec{c}=2\hat{i}+\hat{j}+3\hat{k}\). Let \(\vec{v}\) be the vector in the plane of the vectors \(\vec{a}\) and \(\vec{b}\), such that the length of its projection on the vector \(\vec{c}\) is \(\frac{1}{\sqrt{14}}\). Then \(|\vec{v}|^2\) is equal to

[JEE Main 2026, 24 Jan (Shift 2)]