Angle between vector and z-axis

[Syrus]

1. Homework Statement

I am looking at problem 2.2 pictured above.
I have solved all portions of the question except the last part, which asks for the angle between the normal vector to the surface and the z-axis.
I am aware that the normal vector is simply equal to the gradient of the surface given (the L.H.S. of the equation in the second line of the problem statement. In order to find the angle between this normal and the z-axis (for which I am using the vector (0,0,1), I am using the familiar dot product-cosine relation: a•b = |a| |b| cos(x)

Homework Equations

The Attempt at a Solution

 

[Ray Vickson]

View attachment 110018 1. Homework Statement

I am looking at problem 2.2 pictured above.
I have solved all portions of the question except the last part, which asks for the angle between the normal vector to the surface and the z-axis.
I am aware that the normal vector is simply equal to the gradient of the surface given (the L.H.S. of the equation in the second line of the problem statement. In order to find the angle between this normal and the z-axis (for which I am using the vector (0,0,1), I am using the familiar dot product-cosine relation: a•b = |a| |b| cos(x)

Homework Equations

The Attempt at a Solution

Do not post images (especially do not post them sideways!). Just type out the problem; it is simple enough and does not need a lot of work.

 

[Syrus]

Anyone care to provide a meaningful response?

 

[LCKurtz]

Not me. I'm not willing to lie down to read it.