1. ## Directional Derivatives

Find equations of the tangent plane and normal line to the surface at the point (-8, 0, 0).
Tangent Plane: (make the coefficient of z equal to 1).
__________________________.
Normal line: ____,____
____ ,_____ , .

Thanks!

2. Originally Posted by jffyx
Find equations of the tangent plane and normal line to the surface at the point (-8, 0, 0).
Tangent Plane: (make the coefficient of z equal to 1).
__________________________.
Normal line: ____,____
____ ,_____ , .

Thanks!
Take $F(x,y,z) = xe^y \cos z - z$

the tangent plane is given by: $F_x(-8, 0, 0)(x + 8) + F_y(-8, 0, 0)(y - 0) + F_z(-8, 0, 0)(z - 0) = 0$

the normal line is given by: $\left< -8,0,0 \right> + t \left< \text{normal vector to the above plane} \right>$

3. How do you find the normal vector to the plane?

4. Originally Posted by jffyx
How do you find the normal vector to the plane?
when a plane is written in the form: $ax + by + cz + d = 0$

the normal vector is given by: $\vec n = \left< a,b,c \right>$

remember, you want to write it in the form where c = 1