A line L in three space passes though the origin and intersects the plane (pi) perpendicularly at the point (-3,5,2). Determine the parametric equation of the line L and the scalar equation of the plane (pi)

You know that the line has direction numbers (-3,5,2)

So does the plane.

Did you know?

Did you know that in three-dimensional space, a line that passes through the origin and intersects a plane perpendicularly is known as a normal line? In this case, the normal line, denoted by L, intersects the plane, denoted by (pi), at the point (-3,5,2). The parametric equation of the line L can be determined by considering the direction vector originating from the origin to the point of intersection. On the other hand, the scalar equation of the plane (pi) can be determined by using the coordinates of the point of intersection as well as the coefficients of x, y, and z in the equation. This understanding of lines and planes in three-dimensional space is fundamental in various fields, including mathematics, physics, and engineering.