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

[spoc21]

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

N/A

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

 

[jtyler05si]

To me that would mean the z-value is constant and also the y value. You can pick any point for x

 

[spoc21]

so would the (0,1,1) work?

 

[spoc21]

bump..anyone?

 

[jtyler05si]

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)

 

[Mark44]

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.

 

[spoc21]

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..

 

[Mark44]

Yes, the direction of the line has to be <1, 0, 0> or some scalar multiple of this vector.