# Thread: Points equidistant from planes

1. ## Points equidistant from planes

Find all points that are equidistant from 6x-12y+15z-9=0 and 12x+9y-20z-19=0.

Thanks.

2. ## Re: Points equidistant from planes

Ops, wrong section, this should be in geometry.

3. ## Re: Points equidistant from planes

I would say that since the points are equidistant from the two planes, then they would be equidistant from their normal vectors...

4. ## Re: Points equidistant from planes

Hello, kicma!

$\displaystyle \text{Find all points that are equidistant from }\,6x-12y+15z-9\:=\:0$
$\displaystyle \text{ and }\,12x+9y-20z-19\:=\:0.$

Code:
                  :
*           :           *
*        :        *
*     :     *
*  :  *
- - - - - - - * - - - - - - -
*  :  *
*     :     *
*        :        *
*           :           *
:
The solution is a pair of perpendicular planes
bisecting the angles formed by the two given planes.