Step 1: A rigid body rotates with angular velocity ω = (0, 0, 3) rad/s about the z-axis. Its inertia tensor (in kg·m²) is I = [[2, 0, 0], [0, 3, 0], [0, 0, 1]]. Find the angular momentum vector L. Step 2: Use the tensor relation L_i = Σ_j I_ij·ω_j (matrix multiplication of the tensor by the vector). Step 3: L_x = 2×0 + 0×0 + 0×3 = 0. Step 4: L_y = 0×0 + 3×0 + 0×3 = 0. Step 5: L_z = 0×0 + 0×0 + 1×3 = 3. Step 6: So L = (0, 0, 3) kg·m²/s, parallel to ω here because ω is along a principal axis. Result: If instead ω = (1, 1, 0), then L = (2, 3, 0) — no longer parallel to ω, which is exactly why the tensor (not a scalar) is needed.