Finding a Tangent Plane on a 3D Surface

In summary, the conversation is about a surface with the equation x^2 + 2y^2 + 3z^2 = 12 and a perpendicular plane tangent to the line x = 1 + 2t, y = 3 + 8t, z = 2 - 6t. The speaker realizes they missed something on the answer key and is now questioning how the teacher arrived at the point (1,2,-1) using the parametric equations and taking the derivative of F(x,y,z).
  • #1
Spectre32
136
0
Ok I have a surface withthe eqn of x^2 + 2y^2 +3z^2 = 12. The question tells us that there is a perpendicular plane tangent to the the line is as follows:

x = 1 + 2t
y = 3 + 8t
z = 2 - 6t
 
Last edited:
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  • #2
Whoops I neglected to see something on his answer key... I see what's going on.. Nevermind
 
  • #3
lol .. ok now i have question. After looking at the real solution my teacher used the Para eqn's to make a vector... athen took the derivite of F(x,y,z) and got <2x,4y,6z>. Then he gets this point (1,2,-1)... I'm unclear as to how he got this point.
 
  • #4
Yeah I'm been crackin away at this for a while and i sitll don't get it, anyone anyone anyone..
 

1. How do I find a point on a 3D surface?

To find a point on a 3D surface, you will need to know the coordinates of the surface's vertices. These can be determined using a coordinate system such as Cartesian coordinates. Once you have the coordinates, you can use mathematical equations or algorithms to calculate the specific point you are looking for.

2. Can I use software to help me find a point on a 3D surface?

Yes, there are many software programs available that have tools specifically designed for finding points on 3D surfaces. These programs use advanced mathematical algorithms and visualization techniques to help you locate and manipulate points on a 3D surface.

3. What is the difference between finding a point on a 3D surface and finding a point in 3D space?

While both involve working with three-dimensional coordinates, finding a point on a 3D surface specifically refers to locating a point on a surface that has a defined shape and boundaries. Finding a point in 3D space can refer to locating a point anywhere within a three-dimensional coordinate system, including within a 3D surface.

4. Are there different methods for finding a point on a 3D surface?

Yes, there are various methods for finding a point on a 3D surface, including using mathematical equations, algorithms, or software tools. The most appropriate method will depend on the specific 3D surface and the desired outcome.

5. What are some real-world applications for finding points on 3D surfaces?

Finding points on 3D surfaces has many practical applications, such as in computer graphics, engineering, architecture, and geology. It can be used to model and design objects, analyze and manipulate terrain data, and create realistic visualizations of 3D environments.

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