How to find a vector parallel to a line?

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Homework Help Overview

The discussion revolves around finding a vector that is parallel to a given line represented by the equation x+2 = 1/2y = z-3, which falls under the subject area of vector mathematics and geometry.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to understand how to derive the parallel vector from the line equation and expresses confusion regarding the solution provided in the book.
  • Some participants suggest looking at a related line equation to identify the changes in coordinates that correspond to the vector's components.
  • There is a question raised about the role of the constants in the equation and their impact on the position of the line.

Discussion Status

The discussion is active, with participants exploring the relationship between the line's equation and the resulting vector. Some guidance has been offered regarding the interpretation of the equation, and there appears to be a productive exchange of ideas without a definitive consensus yet.

Contextual Notes

Participants are navigating the implications of the line's equation and how shifts in position affect the identification of the parallel vector. There may be assumptions about familiarity with vector representation and line equations that are not explicitly stated.

r_swayze
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How do I find the vector parallel to the line x+2 = 1/2y = z-3 ?

the book says its < 1,2,1 > but I have no idea how to get there?
 
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Hi r_swayze! :smile:

Just go for the obvious …

that line is parallel to the line x = 1/2y = z, from which it's pretty obvious that if you increase x by 1, the you increase y by 2, and z by 1 :wink:
 
oh I think I see now, so the +2 and -3 from the x and z equations are just telling the shift in position?
 
Yup! :biggrin:
 

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