Question

Find a vector function that represents the curve of intersection ofthe two surfaces. The cylinder

Answer 1

You're already given $x(t)=6\cos t$ and $y(t)=6\sin t$. To find the $z$ component, plug these into the second equation:

$z=xy=36\sin t\cos t=18\sin(2t)$

so we have

$\vec r(t)=6\cos t\,\vec\imath+6\sin t\,\vec\jmath+18\sin(2t)\,\vec k$

Answer 2

Answer:

here'

Step-by-step explanation: