Determining perpendicular planes

[frusic]

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.

 

[Dick]

Isn't the definition of two planes being perpendicular that their normal vectors are perpendicular?

 

[frusic]

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.

 

[Dick]

Aren't (-2, 1, 4) and (1, -2, 1) the normal vectors?

 

[JG89]

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.

 

[frusic]

Thanks Dick and JG, it makes sense! I think I was making it harder than it actually was :)