If two vectors \(\vec{P}=\hat{i}+2m\hat{j}+m\hat{k}\) and \(\vec{Q}=4\hat{i}-2 \hat{j}+m \hat{k}\) are perpendicular to …

If two vectors \(\vec{P}=\hat{i}+2m\hat{j}+m\hat{k}\) and \(\vec{Q}=4\hat{i}-2 \hat{j}+m \hat{k}\) are perpendicular to each other. Then, the value of \(m\) will be:

[JEE Main 2022, 28 July (Shift 2)]