Understanding Planes Perpendicular to Horizontal and Vertical Planes

This question delves into the fundamental concepts of spatial geometry and projection, specifically concerning the orientation of different planes. We need to identify the type of plane that is simultaneously perpendicular to both the horizontal plane (often denoted as $HP$) and the vertical plane (often the frontal plane, denoted as $VP$).

Defining Principal Planes in Descriptive Geometry

In engineering drawing and descriptive geometry, we typically work with three principal projection planes:

• Horizontal Plane ($HP$): This is a flat surface oriented horizontally, parallel to the ground.
• Vertical Plane ($VP$): This is a flat surface oriented vertically. Usually, we consider the Frontal Plane as the primary vertical plane, representing the front view.
• Profile Plane ($PP$): These are vertical planes that are perpendicular to both the $HP$ and the $VP$ (Frontal Plane). They are used to represent side views.

Analyzing the Condition: Perpendicularity to Both Planes

Let's break down the condition that a plane must be perpendicular to both the horizontal plane and the vertical plane:

• Perpendicular to the Horizontal Plane ($HP$): Any plane that is perpendicular to the $HP$ must be oriented vertically. Think of a wall as being perpendicular to the floor ($HP$).
• Perpendicular to the Vertical Plane ($VP$): If a plane is also perpendicular to the vertical (Frontal) plane ($VP$), it means this plane must be oriented sideways, along the direction that is perpendicular to the front view. These are the planes that contain the left-right dimensions and are oriented to show side views.

A plane that satisfies both conditions – being vertical (perpendicular to $HP$) and also perpendicular to the frontal $VP$ – is precisely the definition of a profile plane.

Evaluating the Options

Based on the analysis, let's look at the given options:

• Auxiliary Planes: These are planes other than the principal planes, often used to show the true shape of inclined surfaces. They are not necessarily perpendicular to both $HP$ and $VP$.
• Oblique Planes: These planes are inclined and are neither parallel nor perpendicular to the principal planes ($HP$, $VP$).
• Reference Planes: This term usually refers to the principal planes ($HP$, $VP$, $PP$) themselves, which serve as references for projections. While profile planes are reference planes, not all reference planes fit the specific condition.
• Profile Planes: As discussed, these are vertical planes oriented perpendicular to both the horizontal ($HP$) and frontal vertical ($VP$) planes. They represent side views and perfectly match the question's criteria.

Conclusion

Therefore, the planes which are perpendicular to both the horizontal plane and the vertical plane are known as profile planes.