Understanding Tangent Vectors for Discs: Deciphering (1 -1 0)T

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SUMMARY

The discussion centers on understanding how the vector (1, -1, 0)T represents the tangent axis to a disk at point Q. Participants clarify that this vector is indeed parallel to the tangent vector at Q, confirming that both terms refer to the same concept. The confusion arises from the interpretation of vector addition and the properties of parallel vectors. Ultimately, the consensus is that (1, -1, 0)T is sufficient to describe the tangent direction at the specified point.

PREREQUISITES
  • Understanding of vector mathematics, specifically tangent vectors
  • Familiarity with the concept of parallel vectors
  • Basic knowledge of coordinate systems in three-dimensional space
  • Experience with vector addition and its geometric interpretations
NEXT STEPS
  • Study the properties of tangent vectors in differential geometry
  • Learn about vector translation and its implications in physics and engineering
  • Explore the relationship between radial and tangent vectors in circular motion
  • Investigate applications of tangent vectors in computer graphics and simulations
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Students of mathematics, physics enthusiasts, and anyone studying vector calculus or differential geometry will benefit from this discussion.

Leb
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Homework Statement



I do not understand how the vector (1 -1 0)T represents the axis tangent to the disk at Q.

35ks6jr.jpg


The Attempt at a Solution



Tried thinking in terms of simple vector addition, but just got another vector in the radial direction...
I mean, (1 -1 0)T is parallel to a tangent vector to Q, is that sufficient ?
 
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Hi Leb! :smile:
Leb said:
I do not understand how the vector (1 -1 0)T represents the axis tangent to the disk at Q.
…
Tried thinking in terms of simple vector addition, but just got another vector in the radial direction...
I mean, (1 -1 0)T is parallel to a tangent vector to Q, is that sufficient ?

I don't really understand what's worrying you. :confused:

don't "the axis tangent to the disk at Q" and "parallel to a tangent vector to Q" mean the same thing?
 
tiny-tim said:
Hi Leb! :smile:


I don't really understand what's worrying you. :confused:

don't "the axis tangent to the disk at Q" and "parallel to a tangent vector to Q" mean the same thing?

Hello tiny-tim!

Apparently I was a bit rusty with vectors and was not sure if we are free to translate to parallel vectors on top of each other, but thanks !
 

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