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:
3. Which of the points A(-4, 0,-1), B(3, 1, -5), and C(2, 4, 6) is closest to the yz-plane? Which point lies in the xz-plane?
Question Copy Pasted:
3. Which of the points As24, 0, 21d, Bs3, 1, 25d, and Cs2, 4, 6d is closest to the yz-plane? Which point lies in the xz-plane?
Question:
4. What are the projections of the point (2, 3, 5) on the xy-, yz-, and xz-planes? Draw a rectangular box with the origin and (2, ,3 , 5) as opposite vertices and with its faces parallel to the coordinate planes. Label all vertices of the box. Find the length of the diagonal of the box.
Question Copy Pasted:
4. What are the projections of the point (2, 3, 5) on the xy-, yz-, and xz-planes? Draw a rectangular box with the origin and s2, 3, 5d as opposite vertices and with its faces parallel to the coordinate planes. Label all vertices of the box. Find the length of the diagonal of the box.
16 сен 2024
