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

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