Find the equations of the tangent plane and the normal line to the given surface

Quote:

Originally Posted by Rhode963

Find the equations of the tangent plane and the normal line to the given surface at the given point...

$z=e^xcos(y), (0,0,1)$

I just need a check of my work, I'm studying for my test, and this problem isn't in the back of the book to check.

$z_x=e^x{\color{red}{\cos y}}|(0,0) =1$
$z_y=-e^xsin(y)|(0,0) =0$

So plugging into the plane formula, I got
$z-1=1(x-0)+0(y-0)z =x+1$

${\color{red}{z-1=1(x-0)+0(y-0) =x}}$

And the normal vector would be
<1,0,-1> (this I'm unsure of)
Thus giving parametric line equations of...
$x=t, y=0, z=1-t$

A couple of typo's - in the above in red. The rest is OK.