“Vectors and Planes” is an app by developers of GraphMath Graphing Calculator. It is fully compatible with iOS 14 and 15, mostly compatible with iOS 13 and Mac OS, and performs the following: Provides results and, in most cases, formulas for: 1. Vector magnitude. 2. Angle between vectors. 3. Equation of a plane from 3 given points. 4. Distance between a point and a plane. 5. Point projection on a plane. 6. Angle between a vector and a plane. 7. Angle between two planes. 8. Line of intersection between two planes. 9. Determination of mode of intersections between three planes. Matrix transformations are shown step by step. 10. Calculation of intersection point, when single point is present. Matrix transformations are shown step by step. 11. Circle of intersection between a sphere and a plane. 12. Circle and plane of intersection between two spheres. 13. Volume and surface area of an ellipsoid. 14. Center, major radius, and minor radius of intersection of an ellipsoid and a plane. Provides graphs for: 1. Two vector combination, their sum, difference, cross product, and angle. 2. A plane defined by three points. 3. A plane defined by an equation. 4. A plane and a point combination. 5. A plane and a vector combination. 6. Two plane combination. 7. Three plane combination. 8. A sphere defined as center and radius. 9. A sphere and a plane combination. 10. Two sphere combination. 11. An ellipsoid. 12. An ellipsoid and a plane combination. 13. Two ellipsoid combination. Graph features: 1. Images can be rotated around X, Y, and Z axes and tilted up or down. 2. Images can be drawn with or without perspective. 3. Animated rotation around Z axis is shown on initial drawing. This can be turned off. 4. Structures obscured by planes, spheres or ellipsoids are drawn in grey. 5. Zoom in and out. 6. Scroll function. Previous entries for vectors, planes, and points are stored in a table and available after the app is closed. Tables of points and vectors can be sorted by X, Y, Z, or by most recent. Table of planes can be sorted by A, B, C, D, or by most recent. Provides links to three other apps by same developers: 1. “GraphMath” Graphing Calculator. 2. “Matrix Solver Step by Step" Linear Algebra Visual Guide. 3. “Polynomial and Linear Systems” Equation Solver. Developers hope to get feedback from users at graphmath@aol.com.
