This lecture covers the concept of projecting a vector onto a frame, including the calculation of the horizontal and vertical components. It explains the process step by step, from defining the frame to determining the unit vectors and calculating the projections. The instructor demonstrates how to find the horizontal and vertical components of a vector in a Cartesian frame, emphasizing the importance of understanding the trigonometric functions involved. The lecture concludes with a detailed explanation of the projection onto the vertical and horizontal axes, providing a comprehensive understanding of vector projections in a frame.