a line RS is perpendicular to plane p at R. If T is a second point not on. Can RT be perpendicular to plane P?

Lines AB and LM are each perpendicular to plane P. Are AB and LM coplanar?

Plan P is perpendicular to AB at B. Plane Q intersects AB at P. Can Q be perpendicular to AB?

first part:

Suppose you are standing a ruler on the floor, the ruler is RS, and it is perpendicular to the floor.
If T is not along this ruler, could RT be parallel to ruler RS ??? (NO)

2nd:
think of a table with 4 legs.
All the legs would be perpendicular to the table and parallel to each other. Could you imagine a plane containing two of the legs? (YES)

I don't follow the wording of the 3rd question

I wrote the question wrong. its supposed to be

Plan P is perpendicular to AB at B. Plane Q intersects AB at B. Can Q be perpendicular to AB?

depends on your definition of "intersects"

Imagine a wall and the floor, the wall being Q and the floor being P. They would be perpendicular.
Along the wall draw a line AB, with B on the floor and AB perpendicular with the floor.
Does the wall "intersect" the line AB at B, that is, is B on he wall?

To determine if RT can be perpendicular to plane P, we need to understand the properties of perpendicular lines and planes.

1. Line RS is perpendicular to plane P at point R. This means that RS forms a 90-degree angle with every line lying on the plane P at point R. As we are considering a specific point R, any line that passes through R and lies on the plane P will be perpendicular to the plane P. Therefore, RT can be perpendicular to plane P if point T lies on plane P.

2. Lines AB and LM are each perpendicular to plane P. If two lines are each perpendicular to a common plane, it does not necessarily imply that they are coplanar. Two lines are considered coplanar if they lie on the same plane. In this case, AB and LM may or may not lie on the same plane, so we cannot say for certain if they are coplanar without additional information.

3. Plane P is perpendicular to line AB at point B, and plane Q intersects line AB at point P. To determine if Q can be perpendicular to AB, we need to consider the relationship between the two planes. If plane Q is parallel to plane P or lies on plane P, then it cannot be perpendicular to AB. However, if plane Q intersects plane P at an angle (other than 0 or 180 degrees), then it is possible for plane Q to be perpendicular to AB.

In summary,
- RT can be perpendicular to plane P if point T lies on plane P.
- AB and LM may or may not be coplanar, as being perpendicular to a common plane does not guarantee coplanarity.
- Q can be perpendicular to AB if plane Q intersects plane P at an angle other than 0 or 180 degrees.