I don't get these questions

Is there exactly one plane containing two non intersecting lines?

and

if a line is perpendicular to a plane, is it perpendicular to every line in the plane?

I can help explain these questions to you.

Question 1: Is there exactly one plane containing two non-intersecting lines?

In order to answer this question, we need to understand what a plane is and how lines can be related to it. A plane is a two-dimensional flat surface that extends infinitely in all directions. Lines, on the other hand, are one-dimensional and can be thought of as being "contained" within a plane.

Now, let's consider two lines that do not intersect each other. Since a plane is a two-dimensional surface, it may seem intuitive that there should be exactly one plane containing these two non-intersecting lines. However, we have to remember that there are infinite planes in three-dimensional space that can contain these lines.

To better visualize this, you can try drawing two non-intersecting lines on a piece of paper. Then, you can tilt or rotate the paper, and you will notice that the lines are still contained within the plane formed by the paper's surface.

So, the answer to the question is no, there isn't exactly one plane containing two non-intersecting lines. There are countless planes that contain these lines.

Question 2: If a line is perpendicular to a plane, is it perpendicular to every line in the plane?

When we say a line is perpendicular to a plane, it means that the line forms a right angle (90 degrees) with the plane. Now, whether the line is perpendicular to every line in the plane depends on the orientation and arrangement of the lines within the plane.

Consider a plane with multiple lines arranged in different directions. If a given line is perpendicular to the plane, it will be perpendicular to any line within the plane only if those lines are also perpendicular to the plane and share the same point of intersection with the line.

To better visualize this, you can take a sheet of paper and draw a straight line on the paper at any angle. Now, draw multiple other lines on the paper that intersect the first line at various angles. If you draw a line perpendicular to the paper, you will see that it is only perpendicular to the lines that are also perpendicular to the paper and intersect at the same point.

In conclusion, a line that is perpendicular to a plane is not necessarily perpendicular to every line in the plane. It depends on the orientation and arrangement of the lines within the plane.