The line \({\mathrm{L}}_{1}\) is parallel to the vector \(\vec{\mathrm{a}}=-3\overset{^}{\mathrm{i}}+2\overset{^}{\mathr…

The line \({\mathrm{L}}_{1}\) is parallel to the vector \(\vec{\mathrm{a}}=-3\overset{^}{\mathrm{i}}+2\overset{^}{\mathrm{j}}+4\overset{^}{\mathrm{k}}\) and passes through the point \((7,6,2)\) and the line\({L}_{2}\) is parallel to the vector \(\vec{\mathrm{b}}=2\overset{^}{\mathrm{i}}+\overset{^}{\mathrm{j}}+3\overset{^}{\mathrm{k}}\) and passes through the point \((5,3,4)\). The shortest distance between the lines \({L}_{1}\) and \({\mathrm{L}}_{2}\) is :

[JEE Main 2025, 2 Apr (Shift 2)]