Parallel Planes and Points (3D)

In summary, the point A (3,2,-1) is equidistant from two parallel planes, P1 and P2. Using the distance formula, the distance between the point and either plane is 2. To find the equation of P2, a point on the plane must be calculated. This can be done by using the perpendicular vector of P1, which is also the same as the perpendicular vector of P2 or a scalar multiple of it.
  • #1
SolfegeDuck
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Homework Statement



Point A (3,2,-1) is equidistant from two planes (parallel), known as P1 and P2. P1 has the equation 2x-y+2z+4 = 0. Find the equation of P2.


Homework Equations



D = abs val(ax_o + by_o + cz_o + d) divided by sqrt (a^2 + b^2 + c^2)

The Attempt at a Solution



I used the distance formula and figured out that the distance between the point and either plane is 2. But what do I do now? I know that the plane I'm looking for, since it's parallel, has a perpendicular vector that is the same as P1, if not a scalar multiple. But what next? Thanks in advance.
 
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  • #2
Compute a point on the other plane.
 
  • #3
how do i do that?
 

FAQ: Parallel Planes and Points (3D)

What are parallel planes?

Parallel planes are two planes that never intersect, no matter how far they are extended. They have the same slope and will never converge.

How do you determine if two planes are parallel?

To determine if two planes are parallel, you can compare their normal vectors. If the normal vectors are equal, then the planes are parallel. Another method is to find the angle between the two planes. If the angle is 0 degrees, then the planes are parallel.

What is the equation for a parallel plane?

The equation for a parallel plane can be written as Ax + By + Cz = D, where A, B, and C are the coefficients of x, y, and z, respectively, and D is a constant. Another form is the vector form: r = r0 + sv, where r0 is a point on the plane and v is a vector parallel to the plane.

What are collinear points?

Collinear points are points that lie on the same line. They have the same slope and will never intersect. In 3D, collinear points can also be found on parallel planes.

How can you determine if three points are collinear?

To determine if three points are collinear, you can use the slope formula to calculate the slope between each pair of points. If all three slopes are equal, then the points are collinear. Another method is to calculate the area of the triangle formed by the three points. If the area is 0, then the points are collinear.

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