What is the order of increasing magnitudes for the given set of 3D vectors?

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Homework Help Overview

The discussion revolves around ordering a set of five 3D vectors based on their magnitudes. Participants are tasked with determining the sequence from shortest to longest vector length, using the component forms provided.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Some participants suggest using graph paper to visualize the vectors, while others express confusion about how to graph vectors given in component form. There is a mention of applying a modified version of the Pythagorean theorem to calculate magnitudes in three dimensions.

Discussion Status

The discussion is active, with participants exploring different methods for visualizing and calculating vector magnitudes. Some guidance has been offered regarding the representation of vectors and their components, but no consensus has been reached on the ordering of the vectors.

Contextual Notes

Participants are working with the assumption that the vectors are expressed in standard component form, and there is a note about how to interpret vectors that have only one non-zero component.

BrettL789123
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Five vectors are listed below. Select them in order of increasing magnitudes, from shortest to longest. If B is smallest, then A, C, D, and finally E is the largest, enter BACDE (Note: If of equal length, then enter in the order listed.)
A) 17i-23j-23k
B) 22i+30j
C) 18i-28j-26k
D) 37k
E) 36j+23k
 
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Get some graph paper and draw them!
 
how do you graph them? how do you graph one that just gives you 1 number?
 
BrettL789123 said:
how do you graph them? how do you graph one that just gives you 1 number?
They are given in component vector form. "i" represents the unit vector in the x direction, "j" represents the unit vector in the y direction, and "k" represents the unit vector in the z direction. If one number is given that means the vector is directed in only that direction and has no components in the other directions.

To solve the problem, use the modified version of the pythagorean theorem for 3 dimensions.
 
Sorry I hadn't noticed they were 3d.
Ussually when students draw a vector, the definition of the magnitude leaps out at them!
 

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