Which instruments would be affected by excessively low pressure in the airplane's vacuum system?

The heading indicator relies heavily on the airplane's vacuum system for its operation. This instrument typically uses a gyroscope that needs to maintain a certain speed and orientation, which is achieved through the use of a vacuum system. When the pressure in the vacuum system drops excessively low, the gyroscope can become unstable, resulting in incorrect heading information. Consequently, the pilot may be misled about the airplane's actual direction, which can have significant implications for navigation and overall safety.

In contrast, the other instruments listed, such as the airspeed indicator, pressure indicator, and vertical speed indicator, do not depend on the vacuum system for their function. The airspeed indicator operates based on dynamic pressure from the pitot-static system. The pressure indicator provides readings based on absolute or differential pressure, and the vertical speed indicator relies on static pressure changes. Therefore, while low vacuum pressure critically affects the heading indicator, it does not impact the operation of these other instruments.