What is the Differential Length Vector at a Given Point on a Straight Line?

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Homework Help Overview

The discussion revolves around finding the differential length vector \( dl \) at a specific point on a straight line defined by the equations \( y=2x \) and \( z=4y \). The original poster expresses uncertainty about their solution and seeks clarification on their reasoning.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to derive the expression for \( dl \) using the relationships between \( x \), \( y \), and \( z \). Some participants confirm the correctness of the expression while others seek further clarification on specific terms, such as "projection dx on the x-axis."

Discussion Status

The discussion is ongoing, with some participants providing affirmations of the original poster's approach. However, there remains a lack of clarity regarding certain aspects of the problem, particularly the interpretation of the projection term, indicating that further exploration is needed.

Contextual Notes

Participants are navigating potential misunderstandings about the problem's requirements and the implications of the projection on the x-axis. The original poster expresses concern about overthinking the problem, which may reflect the complexity of the concepts involved.

mknut389
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I got an answer for this, but it just doesn't seem correct. Maybe someone could tell me what I am doing wrong, or that I am just over thinking the problem and I am right.

Homework Statement



Write an expression for the differential length vector dl at the point (1,2,8) on the straight line y=2x, z=4y, and having the projection dx on the x-axis


Homework Equations



dl=dxax+dyay+dzaz


The Attempt at a Solution



y=2x, z=4y, therefore z=8x
therefore

dxax+2dxay+8dxaz.

since there are no variables remaining after you take the derivative, dl is then
1ax+2ay+8az

Any help would be amazing, and please excuse me if I am just being a complete idiot.

Thanks
 
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That seems ok to me. So dl=dx(ax+2*ay+8*az). ax, ay and az are the unit vectors in each direction, right?
 
Yes, ax, ay, az are the direction unit vectors. Thanks
 
... I haven't really understood the problem, but i do understand the solution.. can anyone explain more about this problem especially the "projection dx on the x-axis" part..

please help me... i badly needed the explanation..

thanks in advance...
 

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