Vector arithmetic provides an elegant, powerful framework to model, analyze, and solve real-world problems involving quantities with both magnitude and direction, making it foundational to physics, engineering, computer science, and beyond.
This section explores cloud computing applications in vector and arithmetic operations. It visually explains scalar and cross products through plotting and animated results, contrasting scalar versus vector arithmetic. The core focus is the orthogonality of the cross product, demonstrated with various animated examples. These include how torque's direction indicates the axis of rotation, angular momentum, and the orthogonality of Lorentz force and magnetic fields, further illustrated by interactive web demos. The content also covers normal vectors in 3D rendering, surface normal lighting, camera orientation in 3D, and simplified collision detection. Analytical plotting examples include the area of parallelograms and triangles in 3D, and winding order with surface normals.
🎬 Animated result and interactive web
Scalar Arithmetic vs Vector Arithmetic how torque's direction indicates the axis of rotation Angular Momentum-Axis of Rotation Orthogonality of both the particle's velocity and the magnetic field Lorentz Force Orthogonality Demo Lorentz Force Orthogonality 3D Demo The normal vector always stays perpendicular to the plane Surface Normals-The Cross Product in 3D Rendering Surface Normal lighting how the cross product is used to determine a camera's orientation in a 3D scene how the orthogonality provided by the cross product is used in simplified collision detection and response Last updated 10 hours ago