Exercise 33 Page 48

Let's analyze the figures. The first one shows us that line $r$ is perpendicular to plane $M.$ As we can see, line $r$ is perpendicular to both lines from $M$ that it intersects. The other figure shows us that line $t$ is not perpendicular to plane $P,$ and we can see that it is not perpendicular to both of them. Thus, we can complete the definition! To visualize it, we can take a sheet of paper. This will represent the plane. To represent the lines we can use pens. Let's put one of them on the paper sheet. We can pretend that this is a line in the plane. Now we can place another pen so that it is perpendicular to the first one. Notice that we can do it in many different ways.

The second pen is not always perpendicular to the plane. Let's add another pen in the plane! If we want the third one to be outside the plane and perpendicular to both pens on the sheet, there is only one way to do this. Furthermore, this ensures that this pen is also perpendicular to the plane.

We can conclude that a line is perpendicular to a plane if it is perpendicular to every line in the plane that it intersects.