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

Let \(\vec{a}=\overset{^}{i}+2\overset{^}{j}+\overset{^}{k}\) and \(\vec{b}=2\overset{^}{i}+\overset{^}{j}-\overset{^}{k}\). Let \(\overset{^}{c}\) be a unit vector in the plane of the vectors \(\vec{a}\) and \(\vec{b}\) and be perpendicular to \(\vec{a}\). Then such a vector \(\overset{^}{c}\) is: