(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the parametric surface r(u,v)=<vsinu, vcosu, v^2>

a) Identify the shape of the surface

b) The point (1,1,2) is on the surface. Find:

i) A grid curve wit hv constant that contains this point

ii) A grid curve with u constant that contains this point

c) Find the tangent vector to both grid curves you just found at the point (1,1,2)

d) Find the angle between the grid curves at the point (1,1,2).

e) Find a parametric equation for the plane containing the wo tangent vectors from part c, and containing the point (1,1,2).

f) Describe the relationship between the plane and the surface.

2. Relevant equations

Dot product. And n[tex]\cdot[/tex](r-r[tex]_{0}[/tex])=0.

3. The attempt at a solution

For a-c I am pretty confident that my answers are right, but d-f is where I need some help.

a. Paraboloid

b.

i. <[tex]\sqrt{2}[/tex]sinu, [tex]\sqrt{2}[/tex]cosu, 2>

ii. <v[tex]\frac{\sqrt{2}}{2}[/tex], v[tex]\frac{\sqrt{2}}{2}[/tex], v[tex]^{2}[/tex]>

c. <[tex]\sqrt{2}[/tex],0,2> and <[tex]\frac{\sqrt{2}}{2}[/tex], [tex]\frac{\sqrt{2}}{2}[/tex], 2>

d. I used the definition of the dot product, and dotted i and ii, using [tex]\frac{\pi}{4}[/tex] as u, and [tex]\sqrt{2}[/tex] as v. I got that [tex]\theta[/tex]=0, which doesn't seem right to me.

e. I'm not sure on this one either. I could perhaps the second equation that I posted, but I don't know what I'd use for n.

f. Since I'm not sure on e, I'm not sure of f. As soon as I know e though, I'm sure I can do f.

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# Homework Help: Grid Curves

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