Explore vectors in 3D space through a comprehensive video lecture covering Stewart Calculus Chapter 12. Learn about points in 3D space, distance formulas, and spherical equations with practical examples. Discover how to calculate distances from points to axes, determine unit vectors, and assess vector parallelism. Delve into vector operations, including magnitude, resultant forces, and tension calculations in static equilibrium scenarios. Master the dot product concept and its applications in finding angles between vectors and perpendicular unit vectors. Apply vector knowledge to real-world problems involving torque and force calculations. Investigate the relationships between intersecting lines and planes in 3D, including parallel and orthogonal configurations. Conclude by learning to determine acute angles between lines and planes, providing a solid foundation in 3D vector mathematics.