Determining perpendicular planes

In summary, to determine whether two planes are perpendicular, we need to compare their normal vectors. If the dot product of the normal vectors is 0, then the planes are perpendicular. Otherwise, they are not perpendicular. The normal vectors can be found by looking at the coefficients of the variables in the equations of the planes.
  • #1
frusic
3
0
Determine whether the planes are perpindicular

(-2, 1, 4) . (x-1, y, z+3) = 0 (PLANE A)
(1, -2, 1) . (x+3, y-5, z) = 0 (PLANE B)



Here's what I have figured out so far:

Plane A passes through (1,0,-3) and is perpendicular to (-2,1,4)
Plane B passes through (-3, 5, 0) and is perpendicular to (1, -2, 1)

I know that if I had to determine if they were parallel, (1,0,-3) and (-2,1,4) would have to be along the lines of (-1, 2, 4) and (2, -4, -8).

I'm not sure if I'm on the right track and missing something right in front of me, or completely lost altogether.
 
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  • #2
Isn't the definition of two planes being perpendicular that their normal vectors are perpendicular?
 
  • #3
Yes I'm sure, but I'm not sure what the numbers of perpindicular normal vectors look like.

Like, the example of parallel vectors I gave above - I recognize those as being parallel, but I'm not sure how to tell if something is perpendicular unless the vectors are drawn out.
 
  • #4
Aren't (-2, 1, 4) and (1, -2, 1) the normal vectors?
 
  • #5
If they're perpendicular then the angle between then is 90 degrees. Then their dot product is |normal vector 1||normal vector 2|*cos90 = |normal vector 1||normal vector 2|*0 = 0. So they're perpendicular if their dot product is 0.
 
  • #6
Thanks Dick and JG, it makes sense! I think I was making it harder than it actually was :)
 

1. What is the definition of perpendicular planes?

Perpendicular planes are two planes that intersect each other at a right angle, forming a 90-degree angle.

2. How can you determine if two planes are perpendicular?

To determine if two planes are perpendicular, you can check if their normal vectors are perpendicular. If the dot product of the two normal vectors is equal to 0, then the planes are perpendicular.

3. Can two planes be perpendicular if they are parallel to each other?

No, two planes cannot be perpendicular if they are parallel to each other. Perpendicular planes must intersect each other at a right angle.

4. What is the importance of determining perpendicular planes in geometry?

Determining perpendicular planes is important in geometry because it helps us understand the relationship between different planes in 3-dimensional space. It also allows us to solve problems involving angles and distances between planes.

5. Are there any real-life applications of perpendicular planes?

Yes, perpendicular planes have many real-life applications. For example, architects and engineers use the concept of perpendicular planes to design buildings and structures, and pilots use it to navigate their planes in the air. It is also important in fields such as computer graphics and 3D modeling.

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