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

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The discussion focuses on ordering five 3D vectors by their magnitudes from shortest to longest. The vectors are given in component form, with "i," "j," and "k" representing the x, y, and z directions, respectively. To determine the order, the modified Pythagorean theorem for three dimensions is applied. Participants suggest that graphing the vectors can help visualize their magnitudes, especially for those with only one component. The final order of magnitudes is B, A, C, D, E.
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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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