In Geometric Algebra, the degenerate-metric algebra G(3,0,1) is known as the Projective Geometric Algebra (PGA) for 3D space (3DPGA). In PGA, there is a point-based geometric algebra (point-based PGA) and a plane-based geometric algebra (plane-based PGA). Both algebras have homogeneous geometric entities for points, lines, and planes. The two algebras of PGA are dual to each other through a new geometric entity dualization operation J_e, which is introduced in this paper as its main subject and contribution. The new dualization J_e is an anti-involution with inverse −J_e = D_e. Using J_e, the dual of a point-based PGA entity is its corresponding plane-based PGA entity representing the same geometry (point, line, or plane) with the same orientation. Using D_e = −J_e, the inverse dual (undual) of a plane-based PGA entity is its corresponding point-based PGA entity with the same orientation. The new dualization operation Je maintains the correct orientation of an entity. J_e is defined by a table of duals that are found empirically by observation to maintain correct entity orientation through the dualization. We define a Hodge star dualization operation to be purely an involution, or else purely an anti-involution, between all basis blades and their dual basis blades. As an anti-involution, J_e is also implemented by algebraic methods using Hodge star dualizations in non-degenerate algebras that correspond to PGA. In the prior literature, there are other definitions for the duals in PGA that may not maintain the correct entity orientation and are different than J_e.