b
\(\overrightarrow{\mathrm{E}}=10 \hat{\mathrm{j}} \cos (6 x+8 z-10 \mathrm{ct})\)

\(\mathrm{B}_{\mathrm{o}}=\frac{\mathrm{E}_{\mathrm{o}}}{\mathrm{C}}=\frac{10}{\mathrm{C}}\)

\(\mathrm{W}=10\, \mathrm{C}\)

\(\because \,\hat E \times \hat B = \hat C\)

\(\left| {\begin{array}{*{20}{c}}
  {\hat i}&{\hat j}&{\hat k} \\ 
  0&1&0 \\ 
  {{B_x}}&{{B_y}}&{{B_z}} 
\end{array}} \right| = \frac{{6\hat i + 8\hat j}}{{10}}\)

\( \Rightarrow {B_z}\hat i + 0\hat j - {B_x}\hat k = \frac{3}{5}\hat i + \frac{4}{5}\hat j\)

\({B_z} = \frac{3}{5},\,{{\text{B}}_{\text{y}}} = 0,\,{{\text{B}}_{\text{z}}} = \frac{4}{5}\)

\(\,\therefore \overrightarrow {\text{B}}  = \frac{1}{{\text{C}}}( - 8\widehat {\text{i}} + 6\widehat {\text{k}})\cos (6{\text{x}} + 8{\text{z}} + 10{\text{ct}})\)