What Are the Equations for a Line Through A(3, -1, 2) Parallel to the X-Axis?

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Homework Help Overview

The discussion revolves around finding the vector and parametric equations for a line that passes through the point A(3, -1, 2) and is parallel to the x-axis.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of the line being parallel to the x-axis, questioning what this means for the coordinates of a second point. There is discussion about whether specific points, such as (0, 1, 1), could be used, and participants consider the constancy of the y and z values.

Discussion Status

Participants are actively engaging with the problem, questioning assumptions about the coordinates of points on the line. Some guidance has been offered regarding the nature of the vector that represents the line, indicating that the y and z values should remain constant while the x value can vary.

Contextual Notes

There is some confusion regarding the selection of points and the definition of parallelism in this context, with participants attempting to clarify these aspects without reaching a definitive conclusion.

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Homework Statement

Find the vector/ and parametric equations for the line that passes through A(3, -1, 2) and parallel to the x-axis.

Homework Equations

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The Attempt at a Solution



I know how to find the vector and parametric equations of a line, when given two points. I am just confused on what they mean by parallel to the x-axis. Would we assume the second point is (0,1,1), since it is parallel to the x-axis.. any help is appreciated.. thank you!N
 
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To me that would mean the z-value is constant and also the y value. You can pick any point for x
 
so would the (0,1,1) work?
 
bump..anyone?
 
I don't believe so. Again the y and z terms would be constant.
So any value for {n} can be chosen. Your point would be (n,-1,2)
 
spoc21 said:
so would the (0,1,1) work?
No. If you call this point B, the vector AB is not parallel to the x-axis. A vector parallel to the x-axis has a non-zero x-coordinate, and the other two coordinates are zero.
 
Mark44 said:
No. If you call this point B, the vector AB is not parallel to the x-axis. A vector parallel to the x-axis has a non-zero x-coordinate, and the other two coordinates are zero.

ok, so something like (1,0,0) would work? your point makes sense, just want to confirm..
 
Yes, the direction of the line has to be <1, 0, 0> or some scalar multiple of this vector.
 

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