The Cartesian equation of a line is $2x - 2 = 3y + 1 = 6z - 2$. The vector equation of the line is:

• A
  $\bar{r} = \left(\hat{i} - \frac{1}{3}\hat{j} + \frac{1}{3}\hat{k}\right) + \lambda(3\hat{i} + 2\hat{j} + \hat{k})$
• B
  $\bar{r} = \left(-\hat{i} + \frac{1}{3}\hat{j} - \frac{1}{3}\hat{k}\right) + \lambda\left(\frac{1}{2}\hat{i} + \frac{1}{3}\hat{j} + \frac{1}{6}\hat{k}\right)$
• C
  $\bar{r} = (3\hat{i} - \hat{j} - \hat{k}) + \lambda(3\hat{i} + 2\hat{j} + \hat{k})$
• D
  $\bar{r} = (\hat{i} - \hat{j} + \hat{k}) + \lambda\left(\frac{1}{2}\hat{i} + \frac{1}{3}\hat{j} + \frac{1}{6}\hat{k}\right)$