What Is the Name of u=(3, 3, 3) Vector?

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    Column Vector
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Discussion Overview

The discussion revolves around the representation and naming of the vector u=(3, 3, 3) in R3, including how to visualize it in different dimensions and the distinction between column and row vectors. The scope includes conceptual clarification and technical explanation regarding vector representation in higher dimensions.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • One participant states that u=(3, 3, 3) can be drawn in three-dimensional space, identifying the coordinates as (3, 3, 3).
  • Another participant mentions that there is no general method to draw vectors in n-dimensional space when n>3, suggesting that some components must be ignored or alternative methods used.
  • A different participant identifies u=(3, 3, 3)T as a column vector and seeks clarification on how to draw it.
  • Another participant asserts that the vector is three-dimensional and emphasizes that the distinction between column and row vectors is not relevant for drawing it, discussing projection methods for visualizing the vector in two dimensions.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of the column versus row vector distinction and the methods for visualizing the vector in lower dimensions. The discussion does not reach a consensus on these points.

Contextual Notes

Participants do not clarify the assumptions regarding the projection methods or the specific context in which the vector is being visualized, leaving some aspects unresolved.

DUET
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If u=(3, 3 , 3) is a vector in R3 then we can draw the vector in a three dimensional space.(3=x coordinate, 3= y coordinate, 3= z coordinate.)

if x = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_m \end{bmatrix} is a column vector in Rm then how can we draw it?
In addition we call X = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_m \end{bmatrix} column vector. My question is what is the name of u=(3, 3 , 3) vector?
 
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There is no single, general way to draw a vector of an n-dimensional space on paper if n>3. There might be some interesting methods for specific applications, but you always have to ignore some components, or use other tools like color codes or whatever.

Row vector.
 
I think u=(3, 3 , 3)T is a column vector, three dimensional. How can I draw it now?
 
Yes, it is obviously "three dimensional". Being a "column" vector as opposed to a "row" vector is irrelevant here. You draw such a vector, in two dimensions, by projecting the three dimensional vector onto the two dimensional surface. How you do that depends upon what kind of projection you want to use and, most importantly, from which direction you are looking at the vector.
 

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