Parametric Equation for Line through (1,0,-1) and Parallel to 1/3(x-4)=1/2y=z+2

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Homework Help Overview

The problem involves finding the parametric equation for a line that passes through the point (1,0,-1) and is parallel to another line defined by the equation 1/3(x-4)=1/2y=z+2. The subject area includes vector equations and parametric representations of lines in three-dimensional space.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss how to extract a direction vector from the given line equation and express the coordinates in terms of a parameter. There is uncertainty about the initial steps and how to interpret the line's equation.

Discussion Status

Some participants have offered guidance on interpreting the line equation and have suggested methods for deriving the direction vector. There is an ongoing exploration of how to formulate the parametric equations based on the identified vector.

Contextual Notes

Participants express uncertainty about the initial approach and the lack of examples in the textbook. There is a focus on understanding the relationship between the given line and the point through which the new line must pass.

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Homework Statement



Find the parametric equation for the line through (1,0,-1) and parallel to the line 1/3(x-4)=1/2y=z+2

Homework Equations



Vector equation - r=ro+tv

Perhaps the scaler equation? I'm not entirely sure.

The Attempt at a Solution



I'm not sure where to begin; I don't see any examples in the textbook to go on. I'm not sure if I can read the line given to me and pull out points to use and then create a vector with it.

Thanks
 
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Find the direction vector of the original line from the equations

1/3 (x-4)=t, 1/2 y =t, z+2=t, expressing x, y, z with the parameter t.

ehild
 
So when the line is written with the variables all equal to each other, I am to assume each one is actually equal to t?
 
The above expressions of the coordinates x,y,z are all equal, so each of them is equal to the same number, call it t...

ehild
 
Ah. I read through the text again and I think I understand how to read the equation better. I was looking for a set of points, but really I can get a vector out of it.

Anyway, I believe the answer is:
x= 1+3t
y= 2t
z= -1+t

Hopefully I am correct.
 
Ah. I read through the text again and I think I understand how to read the equation better. I was looking for a set of points, but really I can get a vector out of it.

Anyway, I believe the answer is:
x= 1+3t
y= 2t
z= -1+t

Hopefully I am correct.
 
TrueStar said:
Anyway, I believe the answer is:
x= 1+3t
y= 2t
z= -1+t

Hopefully I am correct.

You are! Good job!

ehild
 

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