$(15$ points$)$ An electromagnetic wave has a magnetic field given by

vec$(B)(z,t)=(3\mathrm{.}0{10}^{-9}(T))hat()cos[(4\mathrm{.}20{10}^{3}ra\frac{d}{m})z+t].$

$($a$)$ In which direction is the wave traveling?

$($b$)$ What is the wavelength of the wave?

$($c$)$ Find the angular frequency $.$

$($d$)$ Write the vector equation for the associated electric field vec$(E)(z,t).$