- To find out the distance between the plane $E_1: 2x+5y+4z=24$ and the plane $E_2:x+5/2 y+2z=12$ we first have to look whether they’re parallel or not, we only can find out the distance if they are parallel.
- In order to find it out we have to compare their normals: Is $n_1=k\cdot n_2$ solvable, then they are parallel.
- $E_1$ and $E_2$ are parallel because k=2.
- Because they are parallel we can use $D=|D_1-D_2 |/|(n_1 )\square|$ (a modified version of the HNF) to find the distance: $D=|24-12|/\sqrt 45=1.789$ units.
I have to summarize the chapter planes for my math lessons but I'm not sure whether this is correct. Can sb help me? Thank you very much!