Why Use i, j, and k as Unit Vectors Instead of x, y, and z?

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Discussion Overview

The discussion revolves around the preference for using i, j, and k as unit vectors to represent the three spatial dimensions in contrast to the more intuitive x, y, and z coordinates. The scope includes conventions in vector notation and the implications for clarity in mathematical expressions.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants note that i, j, and k are preferred because they are conventionally understood as vectors, while x, y, and z are typically seen as coordinates.
  • Others argue that using i, j, and k helps avoid confusion that might arise from using notation like \mathbf{ \hat{x}}, \mathbf{ \hat{y}}, and \mathbf{ \hat{z}}.
  • It is mentioned that i, j, and k are unit vectors, whereas x, y, and z can represent values that extend from minus infinity to plus infinity.
  • A participant reflects on their experience tutoring and acknowledges that unit vectors make sense in this context, indicating a personal preference for the notation.

Areas of Agreement / Disagreement

Participants generally agree that the use of i, j, and k is a matter of convention, but multiple competing views remain regarding the intuitiveness and clarity of using x, y, and z versus i, j, and k.

Contextual Notes

Some assumptions about the clarity and utility of different notations are not fully explored, and the discussion does not resolve the preference for one notation over the other.

tony873004
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Why are i, j, and k perfered in many texts to represent the 3 spatial dimensions instead of (what seems to me to be more intuitive) x, y, and z?
 
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tony873004 said:
Why are i, j, and k perfered in many texts to represent the 3 spatial dimensions instead of (what seems to me to be more intuitive) x, y, and z?
By convention, i, j, k are vectors. x, y, z are coordinates. So you might have (in a cartesian coordinate system)
\textbf{r} = x\textbf{i} + y\textbf{j} + z\textbf{k}
Follow Nabeshin's link for more.
 
It's just a convention. There's no special reason for it, probably other than the fact that they are less confusing than using \mathbf{ \hat{x}} \mathbf{ \hat{y}} and \mathbf{ \hat{z}}
 
By convention, i, j, k are vectors.

More than that, they are unit vectors.

x. y and z extend from minus infinity to plus infinity.
 
Studiot said:
More than that, they are unit vectors.

x. y and z extend from minus infinity to plus infinity.

Sorry, I kinda lost track of this thread, even thought it was my question. I was just tutoring someone in Physics, and her teacher used x-hat, y-hat, and z-hat. But unit vectors make total sense. Thanks everyone for the replies.
 

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