The equation of a line passing through the origin and parallel to the line \[ \vec{r} = 3\hat{i} + 4\hat{j} - 5\hat{k} + t(2\hat{i} - \hat{j} + 7\hat{k}), \] where $t$ is a parameter, is:
(A) $\frac{x}{2} = \frac{y}{-1} = \frac{z}{7}$ (B) $\vec{r} = m(12\hat{i} - 6\hat{j} + 42\hat{k});$ where $m$ is the parameter (C) $\vec{r} = (12\hat{i} - 6\hat{j} + 42\hat{k}) + s(0\hat{i} - 0\hat{j} + 0\hat{k});$ where $s$ is the parameter (D) $\frac{x - 3}{3} = \frac{y - 4}{-4} = \frac{z + 5}{0}$ (E) $\frac{x}{3} = \frac{y}{4} = \frac{z}{5}$
Choose the correct answer from the options given below: