Does the following point lie on plane?

In summary, a plane is a two-dimensional surface that extends infinitely in all directions. To determine if a point lies on a plane, we can use the plane's equation. The equation of a plane is typically written in the form of Ax + By + Cz + D = 0. A point can lie on multiple planes if its coordinates satisfy the equations of more than one plane. Determining if a point lies on a plane is significant in various fields, including geometry, physics, and engineering, as it helps us understand relationships and can be used in calculations and applications.
  • #1
salistoun
14
0
Hi all,

I got this question from a past exam paper does the point (8 , 4 , -5) lie on the plane 7x - 3y + 4z = 8?

Do you work it out as follows because can't find this example in my Linear Algeria book?

7(8) - 3(4) + 4(-5) = 8
56 - 12 - 20 = 8
24 is not equal to 8
Therefore the following point does not lie on the plane.

Thanks
Stephen
 
Physics news on Phys.org
  • #2
you can do that.
 
  • #3
thanks Andrien
 
  • #4
What do you understand the sentence "Ax+ By+ Cz= D is the equation of plane p" to mean?
 
  • #5


I would first like to clarify that Linear Algeria is not a subject within the field of science. However, based on the given information, we can determine that the point (8, 4, -5) does not lie on the plane 7x - 3y + 4z = 8. This is because when we plug in the values for x, y, and z into the equation, we do not get the desired result of 8. Therefore, the point does not satisfy the equation and does not lie on the plane. It is important to accurately solve and interpret mathematical problems in order to draw correct conclusions.
 

1. What is a plane?

A plane is a flat, two-dimensional surface that extends infinitely in all directions. It can be visualized as a flat sheet of paper or a tabletop.

2. How do you determine if a point lies on a plane?

To determine if a point lies on a plane, we can use the plane's equation. If the coordinates of the point satisfy the equation, then the point lies on the plane.

3. What is the equation of a plane?

The equation of a plane is typically written in the form of Ax + By + Cz + D = 0, where A, B, and C are the coefficients of the x, y, and z variables, and D is a constant term.

4. Can a point lie on multiple planes?

Yes, a point can lie on multiple planes. This can happen when the point's coordinates satisfy the equations of more than one plane.

5. What is the significance of determining if a point lies on a plane?

Determining if a point lies on a plane is important in many areas of science and mathematics, such as geometry, physics, and engineering. It can help us understand the relationship between points and planes, and can be used in various calculations and applications.

Similar threads

Replies
2
Views
1K
  • Linear and Abstract Algebra
Replies
1
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
645
  • Introductory Physics Homework Help
Replies
2
Views
307
  • Nuclear Engineering
Replies
7
Views
2K
  • Precalculus Mathematics Homework Help
Replies
7
Views
2K
  • Linear and Abstract Algebra
Replies
4
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
564
  • Precalculus Mathematics Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
Back
Top