1. Find a vector equation that describes the curve of intersection between
the double cone $z^2 = x^2 + y^2$ and the plane $x + y + 2z = 3$.
Hint: The curve is close to a circle, so you might start with
$x = z \cos(t)$, $y = z \sin(t)$
and then do some manipulations to find z in terms of t.