Given vectors P = 3i − 2j − 4k and Q = ni + 2j − k, find the value of n if P and Q are perpendicular.

Two vectors $P$ and $Q$ are perpendicular if their dot product is zero.

$$P \cdot Q = 0$$

$$P = 3i - 2j - 4k$$ $$Q = ni + 2j - k$$

The dot product of two vectors $P = P_x i + P_y j + P_z k$ and $Q = Q_x i + Q_y j + Q_z k$ is given by:

$$P \cdot Q = P_x Q_x + P_y Q_y + P_z Q_z$$

Substitute the components of $P$ and $Q$:

$$P \cdot Q = (3)(n) + (-2)(2) + (-4)(-1)$$ $$P \cdot Q = 3n - 4 + 4$$ $$P \cdot Q = 3n$$

Since $P$ and $Q$ are perpendicular:

$$3n = 0$$ $$n = \frac{0}{3}$$ $$n = 0$$

The value of $n$ is $\boxed{0}$.