This lecture covers the concept of orthogonal projection on a straight line in the context of analytic geometry. Starting with the definition of the projection matrix, the instructor explains how to find the orthogonal projection on any given straight line. The lecture also delves into the symmetrical properties of the projection matrix and provides examples to illustrate the application of these concepts. Through a series of slides, the audience is guided through the process of determining the projection matrix and understanding its significance in geometric transformations.