The equation of line passing through origin and parallel to the line \(\overrightarrow{\mathbf{r}}=3 \hat{i}+4 \hat{j}-5 \hat{k}+\mathrm{t}(2 \hat{i}-\hat{j}+7 \hat{k})\), where t is a parameter, is:

(A) \(\frac{x}{2}=\frac{y}{-1}=\frac{z}{7}\)

(B) \(\overrightarrow{\mathrm{r}}=\mathrm{m}(12 \hat{i}-6 \hat{j}+42 \hat{k})\); where m is the parameter

(C) \(\overrightarrow{\mathbf{r}}=(12 \hat{i}-6 \hat{j}+42 \hat{k})+\mathrm{s}(0 \hat{i}-0 \hat{j}+0 \hat{k})\); where s is the parameter

(D) \(\frac{x-3}{0}=\frac{y-4}{0}=\frac{z+5}{0}\)

(E) \(\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\)

Choose the correct answer from the options given below: