X: Slurry tank stores organic waste mixed with water.
Y: Gas outlet releases methane-rich biogas.
Z: Digester uses anaerobic bacteria to decompose organic material, producing biogas and nutrient-rich slurry for agricultural purposes.
If vector \( \mathbf{a} = 3 \hat{i} + 2 \hat{j} - \hat{k} \) \text{ and } \( \mathbf{b} = \hat{i} - \hat{j} + \hat{k} \), then which of the following is correct?