How to Determine if Points Lie on a Straight Line (12.1.11)

Learn how to find the distance between points and planes. Three-Dimensional Coordinate Systems is the first topic in a typical Calculus 3 (multivariable calculus) course. 3D coordinates provide a method to graph and explore vectors, vector functions, multivariable functions, and many applications. Book: Calculus: Early Transcendentals 8th Edition by James Stewart Current Topic: 12.1 Three-Dimensional Coordinate Systems (1-6 Calculus 1 | 7-11 Calculus 2 | 12-16 Calculus 3) 1. Functions and Models 2. Limits and Derivatives 3. Differentiation Rules 4. Applications of Differentiation 5. Integrals 6. Applications of Integration 7. Techniques of Integration 8. Further Applications of Integration 9. Differential Equations 10. Parametric Equations and Polar Coordinates 11. Infinite Sequences and Series 12. Vectors and Geometry of Space 12.1: Three-Dimensional Coordinate Systems 12.2: Vectors 12.3: The Dot Product 12.4: The Cross Product 12.5: Equations and Planes 12.6: Cylinders and Quadric Surfaces Review 13. Vector Functions 14. Partial Derivatives 15. Multiple Integrals 16. Vector Calculus 17. Second-Order Differential Equations Question: 11. Determine whether the points lie on a straight line. (a) A(2, 4, 2), B(3, 7, -2), C(1, 3, 3) (b) D(0, -5, 5), E(1, -2, 4), F(3, 4, 2) Question Copy Pasted: 11. Determine whether the points lie on a straight line. (a) As2, 4, 2d, Bs3, 7, 22d, Cs1, 3, 3d (b) Ds0, 25, 5d, Es1, 22, 4d, Fs3, 4, 2d