# Cylindrical coordinates of line through a point?

1. Mar 8, 2013

### whig4life

1. The problem statement, all variables and given/known data

Use cylindrical coordinates to describe the line through the point (1,1,0) and parallel to the z-axis.

2. Relevant equations

3. The attempt at a solution

The z-axis is (0,0,1) while the cylindrical coordinates are (√2, ∏/4, z)

Now, is the solution in the form of and r = (√2, ∏/4, 0) + (0,0,1)t? Or am I completely lost? (haha)

Last edited: Mar 8, 2013
2. Mar 8, 2013

### rude man

Draw a line r from the origin to the line x = 1 at some point y. Connect that point with a line r going to the origin.
What is r(y)? Or - hint - r2(y)?
Then, can you express θ in terms of y?
Finally you wind up with f(r) = (const.) + g(θ).

EDIT: oh dear, I assumed the line parallel to the y axis. Never mind ...

Last edited: Mar 8, 2013
3. Mar 8, 2013

### tiny-tim

hi whig4life!
sorry to be pernickety, but no, (0,0,1) is a point, isn't it?

correct
it depends whether you want a parametric equation or an ordinary one

the ordinary equation is r = √2, θ = ∏/4

(just as in cartesian coordinates it would be x = y = 1)

the parametric equation is not (r,θ,z) = (√2, ∏/4, 0) + (0,0,1)t

you can't add non-cartesian coordinates (try adding (1,0,0) to (1,∏,0) … do you get (2,∏,0) ?)

it's (r,θ,z) = (√2, ∏/4, …?… ) ?

4. Mar 8, 2013

### whig4life

I was told: The answer should probably be given in parametric form

r = something, theta = something, z = something

So, any ideas? I've exhausted all my resources trying to look for this maybe a better mind can see it more clearly.

Last edited: Mar 8, 2013
5. Mar 9, 2013

### tiny-tim

hi whig4life!

(just got up :zzz:)

the parametric equation would be r = √2, θ = ∏/4, z = … ?