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:
- A$1$
- B$-1$
- C$-3$
- D$2$
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