3D Coordinate System Homework Exercises

California State University, Northridge - Northridge, CA
Course Name: Calculus III (Math 250)
Professor Name: Dr. Michael Johnson
Assignment Title: 3D Coordinate System Homework Exercises
Submission Date: August 01, 2025


Math 250 3D Coordinate System Homework Exercises
Exercises
1. Point Projection Problem

Question: In a 3D coordinate system, what are the projection points of point P(4, -2,
5) onto the xy-plane, yz-plane, and xz-plane respectively?
Solution:
• The projection onto the xy-plane has z-coordinate 0: (4, -2, 0)
• The projection onto the yz-plane has x-coordinate 0: (0, -2, 5)
• The projection onto the xz-plane has y-coordinate 0: (4, 0, 5)
Answer: Projection onto xy-plane: (4, -2, 0); onto yz-plane: (0, -2, 5); onto xz-plane:
(4, 0, 5)


2. Distance Calculation Between Two Points
Question: Calculate the distance between points A(1, 2, 3) and B(4, 6, 8).
Solution:
Using the distance formula in 3D space:

�(�, �) = (�2 − �1)2 + (�2 − �1)2 + (�2 − �1)2
Substituting the coordinates:

�(�, �) = (4 − 1)2 + (6 − 2)2 + (8 − 3)2 = 32 + 42 + 52 = 9 + 16 + 25 = 50 = 5 2
≈ 7.07

Answer: 5 2 (or approximately 7.07)