The Poynting vector for an electromagnetic wave is given by (left(100 mathrm{~W} / mathrm{m}^{2} ight) sin ^{2}left[left(1000

The Poynting vector for an electromagnetic wave is given by \(\left(100 \mathrm{~W} / \mathrm{m}^{2}\right) \sin ^{2}\left[\left(1000 \mathrm{~m}^{-1}\right) z-\left(3.0 \times 10^{11} \mathrm{~s}^{-1}\right) t\right] \hat{k}\). What are 

\((a)\) the wave's propagation direction and

(b) the time-averaged energy per unit time radiated through a \(1.0-\mathrm{m}^{2}\) surface aligned with its normal parallel to the direction of propagation?

(c) At an instant when the electric field is in the \(+x\) direction, in what direction is the magnetic field? What are 

\((d)\) the wavelength and frequency of this electromagnetic wave and

(e) the electric and magnetic field vectors, as a function of position and time?