Need help with a small vector and parametric question.

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The discussion focuses on determining the vector and parametric equations for the z-axis, which is identified as a line in space. Participants are encouraged to post their attempts at solving the problem in the homework forum, adhering to the provided template. Clarification is sought on the definitions of "vector" and "parametric" equations. Understanding these concepts is crucial for correctly formulating the equations. Engaging with the homework forum and sharing progress is emphasized for effective learning.
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2. Determine vector and parametric equations for the z-axis. (Just so everyone is clear, The z-axis is actually a line in space. So you need to write the vector and parametric equation of this line)
 
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This should be posted in the homework forum along with whatever work you have tried on the problem so far (see the template that pops up when you make a thread)
 
Do you know what "vector" and "parametric" equations mean?
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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