- #1
Michael King
- 10
- 0
Homework Statement
I am just confused about how the question is structured, and I am unsure on how to get the relevant information to answer the question:
Find the angle between the surface normal directions of [tex]r^{2} = 9[/tex] and [tex] x + y + z^{2} = 1 [/tex] at the joined point (2,-2,1)
Homework Equations
I am thinking both the Scalar and Vector product rules, possibly in component form.
The Attempt at a Solution
I begin by stating the definition of [tex]r^{2}[/tex]:
[tex]r^{2} = x^{2} + y^{2} + z^{2}[/tex]
I draw a sphere on paper and indicate the direction of the radius from the origin to the joined point and put the r unit vector following the direction of the radius, and I am really stuck on how to express [tex] x + y + z^{2} = 1 [/tex], and to bring the two together. It has been a LONG summer, and I was thinking that the x,y,z terms could be the components but isn't that function a scalar function? How would I get the normal direction for that? I was thinking of taking the grad of the function then taking the scalar product of the two, but I am stuck on expressing it.