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Planes question

Two planes have vector equations r.(2i+j-3k)=3 and r.(2i+j-3k)=9

Find the distance between them. I'm not too sure how to do this, as I haven't been given a point on the planes? :s-smilie:

Reply 1

aznkid66

Well, note that the plane's normals are the same XD
EDIT: Oh, derp, of course the normals are the same. I obviously need to start reviewing vectors!

Also, if not having a point were the problem, you could just find one. For the first one, there's (0,0,-1), (1,1,0), etc...

(edited 11 years ago)

Reply 2

Felix Felicis

Original post by Music99

Two planes have vector equations r.(2i+j-3k)=3 and r.(2i+j-3k)=9

Find the distance between them. I'm not too sure how to do this, as I haven't been given a point on the planes? :s-smilie:

^As aznkid66 said. Or, you also have the distance of the planes from the origin and you could find the difference between this as the planes are parallel.

Reply 3

Music99

Original post by Felix Felicis

^As aznkid66 said. Or, you also have the distance of the planes from the origin and you could find the difference between this as the planes are parallel.

Makes sense. So with the distance of the plane from the origin its 9 and 3, so the difference is 6, but then what?

Reply 4

Felix Felicis

Original post by Music99

Makes sense. So with the distance of the plane from the origin its 9 and 3, so the difference is 6, but then what?

The distance from the origin isn't 9 and 3. If you have a plane in scalar product form

\mathbf{r} \cdot \mathbf{n} = D

then the distance from the origin is

\dfrac{D}{| \mathbf{n} |}

Reply 5

Music99

Original post by Felix Felicis

The distance from the origin isn't 9 and 3. If you have a plane in scalar product form

\mathbf{r} \cdot \mathbf{n} = D

then the distance from the origin is

\dfrac{D}{| \mathbf{n} |}

Ah yeah, I keep getting confused and thinking i'm dealing with the unit normal vector :P.

Also how would you convert this into scalar product form?

x=-1 +2K + 3D
y=2-K-3D
z=-2+4K+5D

I tried to eliminate K and D but I must be doing it wrong...