A parametric equation is a set of equations that express the coordinates of a point on a curve or surface in terms of one or more parameters. It allows for a more efficient and flexible way to represent a geometric shape or object.
To find the parametric equation for a line segment, you need to know the coordinates of two points on the line segment. Then, you can use the formula x = x1 + t(x2 - x1), y = y1 + t(y2 - y1), and z = z1 + t(z2 - z1), where t is the parameter and (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two points.
The coordinates of the two points needed are the starting point and the ending point of the line segment. In this case, the starting point is (-2, 18, 31) and the ending point is (11, -4, 48).
The parameter for the parametric equation of a line segment is usually denoted by t and represents the distance from the starting point to any point on the line segment. It can take on any real value between 0 and 1, where 0 represents the starting point and 1 represents the ending point.
Yes, parametric equations can be used for any type of geometric shape, including lines, curves, and surfaces. They provide a more efficient and flexible way to represent these shapes, making it easier to perform calculations and make geometric constructions.