In a region of free space, the electric field at an instant of time is $\overrightarrow{\mathbf{E}}=(80.0 \hat{\mathbf{i}}+32.0 \hat{\mathbf{j}}-64.0 \hat{\mathbf{k}}) \mathrm{N} / \mathrm{C}$ and the magnetic field is $\overrightarrow{\mathbf{B}}=(0.200 \hat{\mathbf{i}}+0.080 \hat{\mathbf{j}}+0.290 \hat{\mathbf{k}}) \mu \mathrm{T} .$ (a) Show that the two fields are perpendicular to each other. (b) Determine the Poynting vector for these fields.