Final answer:
The parametric equations of the line passing through (1, 2, 0) and (2, 1, 1) are x(t) = 1 + t, y(t) = 2 - t, and z(t) = t, with t as the parameter.
Step-by-step explanation:
To find the parametric equations of the line passing through the points (1, 2, 0) and (2, 1, 1), we first calculate the direction vector by subtracting the coordinates of the first point from the corresponding coordinates of the second point. The direction vector is (2-1, 1-2, 1-0) = (1, -1, 1).
Next, using one of the points as the reference, say (1, 2, 0), we set up the parametric equations as:
x(t) = 1 + t, y(t) = 2 - t, and z(t) = 0 + t. Here, t is the parameter, which can take any real value.
Therefore, the final parametric equations for the line are:
x(t) = 1 + t, y(t) = 2 - t, z(t) = t.