How to find the Distance Between a Point and Plane/Axis (12.1.12)

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Learn how to find the distance between a point and a plane, and a point and an axis. 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:
12. Find the distance from s4, 22, 6d to each of the following.
(a) The xy-plane (b) The yz-plane
(c) The xz-plane (d) The x-axis
(e) The y-axis (f) The z-axis

Question Copy Pasted:
12. Find the distance from s4, 22, 6d to each of the following. (a) The xy-plane (b) The yz-plane (c) The xz-plane (d) The x-axis (e) The y-axis (f) The z-axis