Vector Addition and Displacement Magnitude in 3D Space

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SUMMARY

The discussion focuses on calculating the components and magnitude of a displacement vector from a base camp to a mountain summit, which is 2450m vertically and 4580m horizontally at an angle of 32.4 degrees west of north. The displacement vector is represented as r = i + j + k, where the x-axis is east, the y-axis is north, and the z-axis is vertical. Participants emphasized the importance of correctly visualizing the 3D coordinate system to solve the problem accurately.

PREREQUISITES
  • Understanding of 3D coordinate systems (x, y, z axes)
  • Knowledge of vector representation and components
  • Familiarity with trigonometric functions for angle calculations
  • Ability to visualize geometric relationships in three dimensions
NEXT STEPS
  • Study vector decomposition in 3D space
  • Learn about trigonometric functions and their applications in vector calculations
  • Explore graphical methods for visualizing 3D vectors
  • Practice problems involving displacement vectors and their magnitudes
USEFUL FOR

Students studying physics or engineering, particularly those focusing on vector analysis and 3D spatial reasoning.

jared69sib
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Homework Statement



The summit of a mountain, 2450m above the base camp, is measured on a map to be 4580m horizontally from the camp in a direction 32.4 degrees west of north. What are the components of the displacement vector from camp to summit? What is its magnitude? Choose the x-axis east, y-axis north, and z axis up.

Homework Equations



vector r = i + j + k

The Attempt at a Solution



I don't think I am drawing the diagram correctly. Not sure where to put z axis. I keep ending up with a triangle. x= 4580, y=2450, bottom angle 32.4...
 
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hi jared69sib! :smile:

the z axis is up,

and the 2450 is between the x and y axes :wink:
 
tiny-tim said:
hi jared69sib! :smile:

the z axis is up,

and the 2450 is between the x and y axes :wink:

Thank you. It was hard to visualize for the very first time.
 

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