Final answer:
Finding the intersection of a plane and a line involves substituting the line's parametric equations into the plane's equation and solving for the parameter. This reveals the intersection point, if it exists.
Step-by-step explanation:
To find the point where a plane and a line intersect, we need to set up a system of equations that represents both the plane and the line.
Usually, a plane is represented by an equation of the form Ax + By + Cz + D = 0, and a line can be represented parametrically by x = x0 + at, y = y0 + bt, and z = z0 + ct where (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector of the line.
To find the intersection, we substitute the parametric equations of the line into the equation of the plane and solve for the parameter t. This gives us the specific values of x, y, and z where the line crosses the plane, if indeed it does intersect.
If there's no solution, then the line does not intersect the plane or is parallel to it. If there are infinite solutions, the line lies entirely in the plane.