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

• Mar 4th 2010, 11:35 AM
Rhode963
Find the equations of the tangent plane and the normal line to the given surface
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.

$z_x=e^x|(0,0) =1$
$z_y=-e^xsin(y)|(0,0) =0$

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

And the normal vector would be
<1,0,-1> (this I'm unsure of)
Thus giving parametric line equations of...
$x=t, y=0, z=1-t$
• Mar 4th 2010, 03:50 PM
Jester
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.