Find equation of plane given curve

[twilit lagoon]

x_Shadow_x

[compact snow]

$\underline{\gamma}(t)=(\ell cos(t), \ell sin(t), sin(kt))$

[twilit lagoon]

x_Shadow_x

[compact snow]

To look at it better

[gloomy canopy]

Couldn’t you just substitute different values of T to get three different points

and then find the plane using the normal vector

[compact snow]

I can try thx, but isn't there another method?

[gloomy canopy]

I’m not sure, this is something I’m familiar with

I graphed it and it doesn’t actually seem to be contained in a plane unless k=0

[compact snow]

especially because it has l as parameter...

k is supposed as 1 so it doesn't care

[compact snow]

oh

this is an exercise from a quiz, and the result says:

"the curve lies always on the cylindric surface [...], lies on the plane {y-lz=0} if and only if k=1, ..."

[gloomy canopy]

That makes sense because lcost, lsint parameterises a circle in the xy plane

I can’t help u with figuring out y-lz=0 but it makes sense in retrospect

[compact snow]

yeah it seems right thinking about it but I don't know the quick procedure to obtain it... anyway thank you!