Applying Vectors to Navigation, Business, and Physics

Miacademy & MiaPrep Learning Channel

This educational video provides a comprehensive overview of how vectors are applied in real-world scenarios across business, navigation, and physics. Moving beyond simple two-dimensional geometry, the lesson introduces vectors in three dimensions and n-dimensions, showing how they can model complex datasets like catering orders where lists of quantities and prices are treated as vectors. The video demonstrates how the dot product can be used to efficiently calculate total costs in such business contexts. The content delves deeply into navigation problems, illustrating how to combine velocity vectors to determine an airplane's ground speed and bearing when affected by wind. It breaks down the process of converting real-world conditions (like wind from the southeast) into vector components, performing vector addition, and interpreting the resultant vector's magnitude and direction. Special attention is paid to the concept of bearings versus standard mathematical angles. Finally, the video applies vectors to physics concepts of force and work. Using a towing example, it guides viewers through calculating the work done by a force applied at an angle. It introduces unit vectors to define direction and uses the dot product to compute work as the product of force and displacement vectors. This video is an excellent resource for connecting abstract vector mathematics to concrete, practical problem-solving in STEM fields.