Orthogonal projection is defined as the process of decomposing a vector V into two components: one that is parallel to another vector W and one that is perpendicular to W. The formula for orthogonal projection is expressed as b - proj b onto a, where 'proj' denotes the projection operation. This concept is visually represented by drawing vectors V and W with their tails together and dropping a perpendicular from the head of W to the line of vector W, forming a right triangle that illustrates the two components. Understanding this geometric representation is crucial for grasping the concept of orthogonal projection.
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