Find the vector equation that represents the curve of intersection of the cylinder x2+y2=1\displaystyle {x}^{{2}}+{y}^{{2}}={1} and the surface z=xey\displaystyle {z}={x}{e}^{{y}}.

Write the equation so the x(t)\displaystyle {x}{\left({t}\right)} term contains a cos(t)\displaystyle {\cos{{\left({t}\right)}}} term.

x(t)=\displaystyle {x}{\left({t}\right)}=  
y(t)=\displaystyle {y}{\left({t}\right)}=  
z(t)=\displaystyle {z}{\left({t}\right)}=