Sketching a simple plane in R3 (should be easy, but not for me :P)

  • Thread starter singleton
  • Start date
  • Tags
    Plane
In summary, the conversation is about learning plane sketching in R3 and specifically, how to draw a plane with the equation 5y-z-10=0. The understanding is that the y intercept will be 2, and the z intercept will be -10, with the absence of an x-term indicating the plane will be parallel to the x-axis. The suggested method is to draw the line 5y-z=10 in the yz-plane and lift it upwards to get the plane. Another method is to use the normal vector a\hat{x}+b\hat{y}+c\hat{z} and visualize it going straight up in the z-direction. The conversation ends with the speaker understanding their mistake in
  • #1
singleton
121
0
Well, I'm learning plane sketching in R3.

One of the questions is 5y- z - 10 = 0

It is my understanding that the y intercept will be 2, and the z intercept will be -10.

With the absence of an x-term it should be parallel (?) to the x-axis.

I sketch the three axis, note the two points (0,2,0) and (0,0,-10) as the intercepts, but I have no idea how to actually draw the plane itself from this point on.

Unfortunately I have no scanner available to me to even show you what I have so far.

If you can even (verbally) suggest how I draw it, that'd be great.
 
Mathematics news on Phys.org
  • #2
To clarify, I have the two points selected, but I just don't understand how I could draw a rectangular section that would be parallel to the x-axis.

It looks...skewed
 
  • #3
x can be anything. if you draw the line 5y-z=10 in the yz-plane & then imagine lifting it straight upwards you'll get your plane.
 
  • #4
An easy way I keep track of planes: if the equation is
[tex]a x + b y + c z = d[/tex]

then a normal vector is
[tex]\vec{n} = a \hat{x} + b \hat{y} + c \hat{z}[/tex]

If you think about it long enough it'll become intuitive. A plane z=constant, is parallel to the xy-plane, so the normal vector goes straight up in the z-direction.
 
  • #5
fourier jr said:
x can be anything. if you draw the line 5y-z=10 in the yz-plane & then imagine lifting it straight upwards you'll get your plane.

aha!

I think I understand it now. I believe that I was going about it the wrong way. It just looked a little funny with the way I drew the x axis. Hard to comprehend three dimensions on a two dimensional paper :D

Later today I'll try and draw it in MSPaint :D
 

1. How do I sketch a simple plane in R3?

To sketch a simple plane in R3, start by choosing two points that lie on the plane. Then, draw a straight line between the two points. Next, choose a third point that does not lie on the same line as the first two points. This third point will be the point where the plane intersects with the z-axis. Finally, use the three points to draw the plane that passes through them.

2. What is the equation for a simple plane in R3?

The equation for a simple plane in R3 is Ax + By + Cz = D, where A, B, and C are the coefficients for the x, y, and z variables and D is a constant. This equation represents all the points that lie on the plane.

3. How many points are needed to uniquely define a plane in R3?

In R3, a plane is defined by three points. This means that if you have any three non-collinear points, you can use them to sketch a unique plane in R3.

4. Can a simple plane in R3 be parallel to any of the coordinate planes?

Yes, a simple plane in R3 can be parallel to any of the coordinate planes. For example, a plane with the equation x = 3 would be parallel to the yz-plane, and a plane with the equation z = 6 would be parallel to the xy-plane.

5. What are some real-world applications of sketching a simple plane in R3?

Sketching a simple plane in R3 is useful in many fields, such as engineering, architecture, and physics. It can be used to represent surfaces, such as building walls or airplane wings, and to visualize vector quantities, such as electric fields or fluid flow.

Similar threads

Replies
1
Views
756
  • Precalculus Mathematics Homework Help
Replies
7
Views
521
Replies
2
Views
998
  • General Math
Replies
12
Views
1K
  • General Math
Replies
3
Views
2K
Replies
12
Views
1K
  • General Math
Replies
6
Views
2K
Replies
2
Views
1K
Replies
2
Views
1K
Replies
1
Views
1K
Back
Top