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    I am not sure how to find the line segment dl to sub into the formula. What I tried was writing dl=dx î+dyĵ +dzk̂ so subbing in x=rcosθ and y=rsinθ and z=z (cylindrical coordinates) gives dl=(-sinθ î+cosθ ĵ + k̂)dθ
    but this does not give the correct answer so I assume this dl is incorrect?

    EDIT: correct question uploaded. THe one I'm looking at is 3c
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    Circle of unit radius in the (x-z) plane means r(t)=(\cos(t),0,\sin(t)) where t is between 0 and 2pi.
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    (Original post by Math12345)
    Circle of unit radius in the (x-z) plane means r(t)=(\cos(t),0,\sin(t)) where t is between 0 and 2pi.
    Thanks! Got it now. But does that mean that the polar co ordinate definitions x=rcostheta and y=rsintheta isn't "strict" so you can e.g. let z- rcostheta or rsintheta and y=0 depending on the question?
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    (Original post by bobbricks)
    Thanks! Got it now. But does that mean that the polar co ordinate definitions x=rcostheta and y=rsintheta isn't "strict" so you can e.g. let z- rcostheta or rsintheta and y=0 depending on the question?

    Yep, it depends which plane the circle is in.

    For example if the plane (half-plane) is \{(x,y,z): y=z \geq 0\} then the semi-circle of radius 2 lying in that half-plane would be parameterised by r(t)=(2\cos(t),\sqrt{2} \sin(t), \sqrt{2} \sin(t)) where t is between 0 and \pi.

    The above parameterisation works because the equation of a circle of radius 2 in 3d is x^2+y^2+z^2=4 which is x^2+2z^2=4 in the plane. Now sub in the components to see this is satisfied.
 
 
 
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