Question

If you were flying an airplane, balloon, or helicopter, why would you need to understand three dimensions to navigate safely?

Answer 1

cause the world around is is three dimensional the air, ground etc.
if it was two dimensional the airplane would only navigate vertically and horizontally and never be able to go up and down.

Answer 2

To determine the effect of obliques forces from the third dimension on the navigation.

Explanation:

When a airplane, balloon, or helicopter flies in air, it is not affected by the planar horizontal and vertical force only. Majorly four forces acts on a plain namely - weight, lift, drag and thrust. It is easy to understand the affect of forces like weight, lift, drag in 2-dimensional space frame but in order to understand the impact of thrust 3-dimensional space frame is required.

Therefore to navigate safely understanding of 3 dimensions is necessary.