Final answer:
The parametric equations of the line through the point (0, -7, 2) and parallel to the given vector are x = 2t, y = -7, and z = 2.
Step-by-step explanation:
To find the parametric equations of a line through a given point and parallel to a given vector, we can use the formula:
x = x0 + at
y = y0 + bt
z = z0 + ct
Where (x0, y0, z0) is the given point and (a, b, c) are the components of the parallel vector. In this case, the given point is (0, -7, 2) and the parallel vector is given by the coefficients of x, y, and z in the equation of the line. So the parametric equations are:
x = 0 + 2t
y = -7 + 0t
z = 2 + 0t