In a region of free space, the elctric field at some instant of time is, `E = (80hati + 32hatj - 64hatk) Vm^(-1)` and the magnetic field is `B = (0.2hati + 0.08hatj + 0.29jhatk)muT`.
(i) Show that these two fields are perpendicular to each other.
(ii) Determine the poynting vector for these fields.

Explanation

To solve the given problem, we will break it down into two parts as specified in the question.

### Part (i): Show that the electric field \( \mathbf{E} \) and magnetic field \( \mathbf{B} \) are perpendicular.

1. **Given Fields**:
- Electric field:
\[
\mathbf{E} = 80 \hat{i} + 32 \hat{j} - 64 \hat{k} \, \text{Vm}^{-1}
...