Final answer:
The parametric equation for a line perpendicular to the xy-plane and passing through the origin is x = 0ˣt, y = 0ˣt, z = cˣt, where t is the parameter and c is a non-zero constant.
Step-by-step explanation:
The parametric equation for a line perpendicular to the xy-plane and passing through the origin can be represented as:
Where t is the parameter and c is a constant not equal to zero. Since the line is perpendicular to the xy-plane, its direction vector must be parallel to the z-axis, which is why there are zeros in the x and y components of the parametric equation, and c represents the rate at which the line moves along the z-axis.