What does î(o) represent in vectors?

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Discussion Overview

The discussion revolves around the notation î(o) in the context of vectors, exploring its meaning and the conventions surrounding vector notation. Participants seek clarification on whether this notation indicates a vector making an angle of 0 degrees with the x-axis and discuss its origins and usage in various contexts.

Discussion Character

  • Exploratory
  • Debate/contested

Main Points Raised

  • One participant questions whether î(o) refers to a vector making an angle of 0 degrees with the x-axis.
  • Another participant suggests that the notation might represent the unit vector in the x direction, with the 'o' indicating the x component of the vector.
  • A participant mentions that the notation may have originated from quaternion notation, which was adapted into vector notation by Gibbs and others.
  • There is a clarification request regarding whether the notation is î(o) or i^0, and whether 'o' is a letter or the number '0'.
  • One participant emphasizes that such notation should be defined in the document where it appears, noting the lack of standard meaning for the notation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the meaning of î(o), and multiple interpretations and uncertainties remain regarding its definition and usage.

Contextual Notes

Participants highlight the importance of context in understanding notation, indicating that the meaning may depend on the specific document or source where it is found.

Kavya Chopra
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This problem is fairly objective (though quite stupid)
What does î(o) represent?
Does it refer to a vector making angle 0 degrees with the x axis?
I searched but couldn't find the answer anywhere. Please help.

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Can you provide some context where you've seen this notation used?
 
Can you provide some context here? What book or video used this notation?

My guess would be the i represents the unit vector in th x direction and the 0 represents the x component of the vector. Similarly for y using j and z using k.

The notation came initially from quaternion notation. Quaternions were extensions of complex numbers into 3 dimensions. When Gibbs and others decided that quaternion math was useful but overly complicated they extracted out the useful part to make vectors and kept the ijk notation.
 
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Kavya Chopra said:
What does î(o) represent?
Did you mean î(o) or ##i^0\,##? And is it an o or a 0?
 
Î(o). o not 0.
 
gneill said:
Can you provide some context where you've seen this notation used?
I came across this while I was doing some questions on vectors.
 
In general, these types of notation need to be defined in the document or book that they appear in. There is no standard meaning of the notation. If the document/book is well done, there will be a summary of notation somewhere. Otherwise, you are forced to scan through the preceding text and try to spot the definition. I always hated the books that required that.
 
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I see. Thanks a lot.
 

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