Projection of Vector on a Plane

1. Projection of any Vector on a given Plane is same as Rejection of that Vector from the Normal to that Plane.
2. Given a Plane having Normal Vector \(\vec{A}\), the Projection Vector \(\vec{P}\) of a Vector \(\vec{B}\) on the Normal of the Plane is given as
   
   \(\vec{P}=\vec{B}_{||}=\frac{(\vec{A}\cdot\vec{B})\vec{A}}{|\vec{A}|^2}\)
   
   Rejection Vector \(\vec{R}\) of Vector \(\vec{B}\) from the Normal to the Plane is given as
   
   \(\vec{R}=\vec{B}_\perp=\vec{B}-\vec{B}_{||}=\vec{B}-\frac{(\vec{A}\cdot\vec{B})\vec{A}}{|\vec{A}|^2}=\frac{\vec{A} \times (\vec{B} \times \vec{A})}{|\vec{A}|^2}\)
   
   The Rejection Vector \(\vec{R}\) is the Projection of Vector \(\vec{B}\) on the Plane.