Final answer:
To find the point of intersection of two lines, set the components of the lines equal to each other and solve for t.
Step-by-step explanation:
To find the point at which two lines intersect, we need to find the values of r and s that satisfy both equations. The given lines are defined as:
r = (2, 2, 0) + t(2, -2, 2)
s = (4, 0, 2) + t(-2, 2, 0)
We can set the x, y, and z components of both lines equal to each other and solve for t to find the point of intersection. By solving the system of equations, we find that the lines intersect at the point (6, -2, 2).