Cylindrical coordinates of line through a point?

[whig4life]

Homework Statement

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

Homework Equations

How does one go about this? Even my course book was unclear about this. Any general overview about how to do such a question will be helpful.

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)

 

[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 ...

 

[tiny-tim]

hi whig4life!

The z-axis is (0,0,1)

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

while the cylindrical coordinates are (√2, ∏/4, z)

correct

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

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, …?… ) ?

 

[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.

 

[tiny-tim]

hi whig4life!

(just got up :zzz:)

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