- #1
Ral
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Homework Statement
a.)[tex]\sqrt{x^2+y^2}[/tex]
Find the equation of the tangent plane at the point given by: x = 1, y = 1
Draw the 3d-graph of the surface and the tangent plane.
[tex]\stackrel{\rightarrow}{n}[/tex] = the normal vector to the tangent plane.
b.) If the surface is intersected with the plane y = 1, what curve do you get?
Find the intersection of the tangent line to the resulting curve when x = 1.
Draw a 2d graph of the curve and the tangent line.
c.) Is the tangent line obtained in part (b) orthogonal to [tex]\stackrel{\rightarrow}{n}[/tex]?
Homework Equations
The Attempt at a Solution
I have part a done.
For the tangent plane, I have:
[tex]z= \frac{2}{\sqrt{2}}(x-1)+\frac{2}{\sqrt{2}}(y-1)+\sqrt{2}[/tex]
and [tex]\stackrel{\rightarrow}{n}=(\frac{2}{\sqrt{2}},\frac{2}{\sqrt{2}},-1)[/tex]
I'm not quite sure what to do for part b. I was also trying to use Maple to do the 3d graph, but that was also confusing me, if possible, can I also see what it's suppose to look like.