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Cylindrical coordinates of line through a point?
- Thread starter whig4life
- Start date
What have you tried? Without seeing your work we don't know where you are stuck.Use cylindrical coordinates to describe the line through the point (1,1,0) and parallel to the z-axis.
Have you sketched what a line parallel to the z-axis looks like? If you pick some point along the line, how do r and theta change?
D
Deleted member 4993
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Use cylindrical coordinates to describe the line through the point (1,1,0) and parallel to the z-axis.
Hint:
How would you describe the point (1,1) in polar co-ordinate?
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Yes, the line is (√2, ∏/4, z).Sorry for keeping this to myself, it was purely an error of ommission--
The z-axis is (0,0,1) while the cylindrical coordinates are (√2, ∏/4, z)
Now, is the solution in the form of r=r0+tv? Or am I completely lost? (haha)
Not sure what the 2nd part of the question is.
In parametric form, r(t) = √2, theta(t) = ∏/4, and z(t) = t
In vector form, r0 = (√2, ∏/4, 0) and r = r0 + (0,0,1)t
Yes, the line is (√2, ∏/4, z).
Not sure what the 2nd part of the question is.
In parametric form, r(t) = √2, theta(t) = ∏/4, and z(t) = t
In vector form, r0 = (√2, ∏/4, 0) and r = r0 + (0,0,1)t
I believe the second part is asking what conditions r,θ, and z need to satisfy.
Yes - write the r in bold to show it is a vector, and NOT the same as the rho or r component in the cylindrical coordinates. In the same vector sense, r0 = (√2, ∏/4, 0) and v = (0,0,1).So am I correct in stating that the answer is: r= (√2, ∏/4, 0) + (0,0,1)t ?