Final answer:
The parametric equations for the line through the point (0, 1, 3) that is perpendicular to the line x = 2t, y = 1 - t, z = 4t are x = 0 - t, y = 1 - 2t, z = 3 - t.
Step-by-step explanation:
To find the parametric equations for the line through the point (0, 1, 3) that is perpendicular to the line x = 2t, y = 1 - t, z = 4t, we need to find the direction vector of the given line. The direction vector is the coefficients of t in the line's equations, which are (2, -1, 4).
Since the line we are looking for is perpendicular to the given line, the dot product between their direction vectors should be zero. Therefore, the direction vector for the line we want is (-1, -2, -1).
Using the point-slope form of a line, the parametric equations for the line through (0, 1, 3) with the direction vector (-1, -2, -1) are x = 0 - t, y = 1 - 2t, z = 3 - t.