A line passes through the point with position vector $2\hat i -\hat j+4\hat k$ and is in the direction of the vector $\hat i +\hat j-2\hat k$. The equation of the line in Cartesian form is:

$\frac{x-2}{1}=\frac{y+1}{1}=\frac{4-z}{2}$

The correct answer is Option (1) → $\frac{x-2}{1}=\frac{y+1}{1}=\frac{4-z}{2}$

Given point: $\vec{r}_0 = 2\hat{i} - \hat{j} + 4\hat{k}$

Direction vector: $\vec{d} = \hat{i} + \hat{j} - 2\hat{k}$

Vector form of line: $\vec{r} = \vec{r}_0 + \lambda \vec{d} = (2\hat{i} - \hat{j} + 4\hat{k}) + \lambda (\hat{i} + \hat{j} - 2\hat{k})$

Cartesian form: $\frac{x - 2}{1} = \frac{y + 1}{1} = \frac{z - 4}{-2}$