The z-component of your cross-product is incorrect:
And so
That should prove much simpler, particularly when you take the norm.
--Kevin C.
Find the parametric representation of the ellipsoid using the Euler's angles. Then calculate the normal vector and the first quatratic form at (1,1,1).
Solution so far:
I use the method I learned in class and got
Now, the normal vector
But I found that , in which is getting a bit ridiculous, am I doing the right thing?