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Is this what you mean? We can just "slice" the vector here to get the coordinate pieces.
sage: var('t')
t
sage: V = vector((cos(t)^3, sin(t)^3, cos(2*t)))
sage: parametric_plot3d(V,(t,0,2*pi))
sage: parametric_plot(V[:2],(t,0,2*pi))
sage: parametric_plot(V[1:],(t,0,2*pi))
sage: parametric_plot(vector((V[0],V[2])),(t,0,2*pi))
Naturally, orthogonal projection to some random plane would be more involved (though basically you could use the vector projection, I guess), but maybe you don't need that much firepower.
