Plücker's Relations are a set of quadratic equations that are the necessary and sufficient conditions for the coefficients in a linear combination of basis r-blades in an n-dimensional vector space to have come from the expansion of a r-blade. The usual derivation is obscure and non-intuitive, making even the writing down of the relations themselves a difficult task. In this paper, a new viewpoint is presented: A r-vector B is an r-blade iff B (.) B~ , tilde denoting reversal, maps scalars to scalars and 1-vectors to 1-vectors; the simple proof uses geometric algebra and explicitly reconstructs the blade; the complicated quadratic Plücker's Relations fall out as a corollary. For the electromagnetic 2-vector in spacetime, Plücker's Relations shed light on a well-known relativistic invariance and result in its explicit decomposition as a wedge product of two vectors in spacetime.