In space how many planes can be perpendicular to a given line at a given point on that line in space

Answer 1

Only one!

Think of it in 2 dimensions: hold up a sheet of paper as the X-Y plane; with the Z axis going directly into the page. Imagine that the given line goes directly into the page, i.e., it's parallel to the z axis. So, we see the given line as a point.

Now, it's easy to see that the only plane perpendicular to the line going into the paper is the X-Y plane, i.e., the sheet of paper, itself.

Answer 2

It's really difficult to think in 3-D, but let's see what we can do.

What does it mean to be perpendicular? 90-degree angles are formed, right? If I take a pencil, push it through a piece of paper and stop at any one point on the pencil, how many positions can that "plane" be in to be perpendicular to the pencil. You tell me.