Which pairs of planes are parallel and distinct and which are conincident?
2x+4y-7z-2=0
4x+6y-14z-8=0

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- IsTim

- chestercat

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- IsTim

I tried looking through my notes and textbook for this one, but unless there is a direct connection, I don't understand how to apply it to this question.

- IsTim

I managed to answer some unrelated questions beforehand, but I don't know how I managed to solve them...

- IsTim

So I figured out the normals were [2,3,7] and [4,6,-14]

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## More answers

- IsTim

I can see that I just have to multiply 2,3,7 by 2 to get the other plane. So would that be conidental or parallel and distinct?

- bahrom7893

- bahrom7893

- IsTim

Wait. Maybe I'll try something out here.

- Zarkon

how is [2,3,7] the normal vector?

- IsTim

Er, I just looked at my notes and inferred that...

- Zarkon

if 2x+4y-7z-2=0 is your equation then <2,4,7> is the normal vector

- Zarkon

<2,4,-7>

- bahrom7893

Zarkon to the rescue!!!!

- IsTim

Ok, got that. For the other then, it must be 4,6,-14?

- Zarkon

yes

- IsTim

So from this, how would I determine the answer? Or do I need more?

- anonymous

if the planes are parrallel then the cross product of their normal vectors should be 0

- Zarkon

two plane are parallel iff their normal vectors are parellel

- IsTim

I'll try that cross product thing. Thanks guys. I'lll cry out if I have a problem.

- Zarkon

two non zero vectors \(\vec{v}\) and \(\vec{u}\) are parallel iff \(\vec{v}=c\vec{u}\) for some scalar \(c\)

- IsTim

Pardon?

- Zarkon

is one of the vectors a constant multiple of the other?

- IsTim

The first one, multiplied by 2, equals the second one.

- Zarkon

really?

- IsTim

IT seemed so...

- Zarkon

if you have the equations
2x+4y-7z-2=0
4x+6y-14z-8=0
then you have the normal vectors
<2,4,-7> and <4,6,-14>
are these constant multiples of each other?

- IsTim

That 4y was suppose to be a 3y....

- IsTim

I did mistype that. No wonder my confusion. And probably yours...

- Zarkon

then <4,6,-14>=2<2,3,-7>
and so they are parallel...and therefore their planes are parallel

- IsTim

And distinct??

- Zarkon

yes

- IsTim

Awesome. Thank you. This was relatively simple after all...

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