If $\mathbf{A}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+8 \hat{\mathbf{k}}$ is perpendicular to $\mathbf{B}=4 \hat{\mathbf{j}}-4 \hat{\mathbf{i}}+\alpha \hat{\mathbf{k}}$, then the value of $\alpha$ is