Question

Statement1: In absence of air, projectile motion is always a 2D motion.
Statement2: In absence of any external force in 3D space, at any time during its flight Projectile's velocity has only two components.

Answer 1

The projectile has velocity in one direction and acceleration in other so it's motion can be only in 2D. Initially velocity has two components in some X-Z plane (suppose). So without any external force in Y direction, it cannot gain any component of velocity. And to be 1D both velocity and acceleration have to be in same direction.