Let C be the curve given by r(t) = <tcos(t), tsin(t), t>.
a) Show that C lies on the cone x^2 + y^2 = z^2 and draw a rough sketch of C on the cone.
b) Use a computer algebra system to plot the projections onto the xy- and yz-planes of the curve r(t) = <tcos(t), tsin(t).
Then for lying on this curve, we have
So that and we can say that the curve lies on the cone
Cone (3D surface) with the curve C (in dotted green) is shown below
b) Projections in XY plane are of the form given below:
Projection in YZ plane is of the form which is given below:
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