How to Find a Plane Equation Parallel to Another Plane?

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In summary, the user is trying to find an equation of a plane through the point (3, -3, -2) that is parallel to the plane −2x+1y+4z=−6 and has a coefficient of x equal to -2. The user has input an equation, -2x+y+4z+23, but it does not go through the given point. They are asking for help on how to approach it differently and it is suggested to use the equation ax + by + cz = 0 and substitute the point in for x, y, and z to ensure it goes through the given point. The user then understands and thanks for the help.
  • #1
krtica
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Q: Find an equation of a plane through the point (3, -3, -2) which is parallel to the plane −2x+1y+4z=−6 in which the coefficient of x is -2.

The website asks you to format the answer equal to zero. My input is -2x+y+4z+23, but it shows wrong. I have checked my answer a couple of times, but am not sure how to approach it differently.
 
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  • #2
Welcome to PF!

Hi krtica! Welcome to PF! :smile:
krtica said:
Q: Find an equation of a plane through the point (3, -3, -2) which is parallel to the plane −2x+1y+4z=−6 in which the coefficient of x is -2.
…
My input is -2x+y+4z+23 …


That doesn't go through (3, -3, -2). :wink:
 
  • #3


tiny-tim said:
Hi krtica! Welcome to PF! :smile:



That doesn't go through (3, -3, -2). :wink:

Thanks!

Isn't the equation for a plane a(x-xi)+b(y-yi)+c(z-zi)=0? Where a,b,c are the vector components?
 
  • #4
Yes, but if you have actual numbers, it's a lot easier to write it as ax + by + cz = …, and just fill in the number so that it fits the given point. :wink:
 
  • #5
By filling in the numbers, do you mean substituting the point in x,y,z? I am not quite sure exactly what you mean, my apologies.
 
  • #6
Yes, substituting the point in ax + by + cz …

then it's bound to go through that point, isn't it? :wink:
 
  • #7
God! Got it.

Thank you, I really do appreciate your help.
 

FAQ: How to Find a Plane Equation Parallel to Another Plane?

1. What is a basic plane equation?

A basic plane equation is a mathematical representation of a plane in 3-dimensional space. It is typically written in the form of ax + by + cz + d = 0, where a, b, and c are the coefficients for the x, y, and z variables, and d is a constant.

2. How do I find the equation of a plane?

To find the equation of a plane, you will need to know at least 3 points on the plane or 2 points and a normal vector. Once you have this information, you can use the point-normal form or the standard form to write the equation of the plane.

3. What is the point-normal form of a plane equation?

The point-normal form of a plane equation is written as (x - x0)a + (y - y0)b + (z - z0)c = 0, where (x0, y0, z0) is a point on the plane and (a, b, c) is the normal vector to the plane.

4. What is the standard form of a plane equation?

The standard form of a plane equation is ax + by + cz + d = 0, where a, b, and c are the coefficients for the x, y, and z variables, and d is a constant. This form is useful for graphing and visualizing the plane.

5. Can a plane equation have more than one solution?

No, a plane equation does not have multiple solutions. It represents a single plane in 3-dimensional space. However, different planes can have the same equation if they are parallel or coincident.

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