Vaguely defined vector related question

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SUMMARY

The discussion centers on the concept of perpendicular vectors, specifically addressing how they can be represented in two distinct ways. Participants suggest demonstrating the anti-commutative property of the cross product, particularly with the example of the unit vectors i, j, and k in three-dimensional space. The cross product i × j = k is highlighted as a clear illustration of perpendicularity. The conversation also raises questions about the specific types of vectors being referenced in the homework statement.

PREREQUISITES
  • Understanding of vector operations, specifically cross products
  • Familiarity with unit vectors i, j, and k in three-dimensional space
  • Knowledge of vector properties, including perpendicularity
  • Basic grasp of anti-commutative properties in mathematics
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  • Research the properties of the cross product in vector mathematics
  • Explore visual representations of vectors in three-dimensional space
  • Learn about the applications of perpendicular vectors in physics
  • Investigate the implications of anti-commutativity in vector operations
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Students studying vector mathematics, educators teaching physics or mathematics, and anyone interested in understanding vector properties and their applications.

FermatPell
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Homework Statement



Vectors can be perpendicular in two ways. Show them!


Homework Equations



none

The Attempt at a Solution



I know a lot about vectors, but I'm just not sure what I'm supposed to do. Maybe demonstrate that cross product is anti-commutative?
 
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Maybe just a picture of a vector with i, j, and k (x,y,z) components, each component of which is mutually perpendicular to the others? The cross product i X j = k is a good one.
 
Hi FermatPell! :smile:
FermatPell said:
Vectors can be perpendicular in two ways. Show them!

I can't think of two ways … perpendicular is perpendicular. :confused:

What type of vectors are they talking about?

(and is that the exact question?)​
 

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