Equation of Plane Containing Point (-1,2,-2) & Satisfying Conditions

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In summary, the problem is to find the equation of a plane that contains the point (-1, 2, -2) and satisfies the conditions of being parallel to the xy plane, orthogonal to the z-axis, parallel to both the x and z axes, and parallel to the plane x-y+3z = 100 (plane A). After finding the normal of plane A to be <1, -1, 3>, it is realized that the first two conditions are equivalent and therefore, a single plane cannot satisfy all four conditions. It is likely that the task is to find different planes that satisfy each of the given conditions.
  • #1
popo902
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Homework Statement


write the equation of the plane that contains the point(-1, 2, -2) and satisfies
1. parallel to xy plane
2. orthogonal to z-axis
3.parallel to both the x and z axes
4. parallel to the plane x-y+3z = 100 (plane A)


Homework Equations





The Attempt at a Solution


i started with finding the normal of plane A which is <1,-1,3>
and i know that the normal of this plane should be the normal of my plane suince they're
parallel
but what i don't get is how the plane I am finding can be orthogonal the the z axizs and parallel to it at the same time...
i drea it and it still doesn't look like it makes sense
i don't know where to go from here...
 
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  • #2
popo902 said:
i started with finding the normal of plane A which is <1,-1,3>
and i know that the normal of this plane should be the normal of my plane suince they're
parallel
but what i don't get is how the plane I am finding can be orthogonal the the z axizs and parallel to it at the same time...
i drea it and it still doesn't look like it makes sense
i don't know where to go from here...

Are you sure you don't need to find planes for each of the conditions? I don't think there is a single plane that satisfies all of those conditions.
 
  • #3
The first two equations are equivalent. A plane that is parallel to the x-y plane is automatically orthogonal to the z-axis.
 
  • #4
now that i think of it...i think i was supposed to find ones that satisfy each.
wow i feel dumb
i was actually stressing about how a plane could bend to meet the reqs :s
 

FAQ: Equation of Plane Containing Point (-1,2,-2) & Satisfying Conditions

1. What is the equation of a plane containing the point (-1,2,-2)?

The equation of a plane is typically written in the form ax + by + cz = d, where a, b, and c are constants and x, y, and z are variables representing the coordinates of a point on the plane. To find the equation of a plane containing the point (-1,2,-2), we need to first determine the values of a, b, and c. This can be done by using the coordinates of the given point and the conditions that the plane needs to satisfy.

2. How do you find the equation of a plane satisfying certain conditions?

To find the equation of a plane satisfying certain conditions, we need to first determine the values of a, b, and c by using the given conditions. These conditions could include things like the plane containing a certain point, being parallel to a certain line or plane, or perpendicular to a certain vector. Once we have determined the values of a, b, and c, we can plug them into the general equation of a plane (ax + by + cz = d) and solve for d to get the specific equation of the plane.

3. Can the equation of a plane be written in different forms?

Yes, the equation of a plane can be written in different forms. In addition to the standard form (ax + by + cz = d), it can also be written in point-normal form (n · (r - r0) = 0) or vector form (r = r0 + s v + t w). These different forms may be more useful in certain situations, but they all represent the same plane.

4. What are the conditions that a plane needs to satisfy?

The conditions that a plane needs to satisfy can vary depending on the given information and situation. Some common conditions include containing a certain point, being parallel to a certain line or plane, or perpendicular to a certain vector. These conditions can be used to determine the values of a, b, and c in the general equation of a plane (ax + by + cz = d).

5. How do you graph a plane given its equation?

To graph a plane given its equation, we can first rewrite the equation in the form z = f(x,y). This will give us the equation of a function in two variables, which we can then graph on a 3D coordinate system. Alternatively, we can find three points that satisfy the equation (by setting x, y, or z to 0) and connect them to create a triangle, which will represent the plane in 3D space.

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