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 2 years ago
Which pairs of planes are parallel and distinct and which are conincident?
2x+4y7z2=0
4x+6y14z8=0
 2 years ago
Which pairs of planes are parallel and distinct and which are conincident? 2x+4y7z2=0 4x+6y14z8=0

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IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0I 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
 2 years ago
Best ResponseYou've already chosen the best response.0I managed to answer some unrelated questions beforehand, but I don't know how I managed to solve them...

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0So I figured out the normals were [2,3,7] and [4,6,14]

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0I 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
 2 years ago
Best ResponseYou've already chosen the best response.0that should be parallel and distinct.. if u can just multiply them by a scalar, but i suck at this, so idk.. @Mertsj @Zarkon

bahrom7893
 2 years ago
Best ResponseYou've already chosen the best response.0@amistre64 @satellite73 @myininaya

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Wait. Maybe I'll try something out here.

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.0how is [2,3,7] the normal vector?

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Er, I just looked at my notes and inferred that...

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.0if 2x+4y7z2=0 is your equation then <2,4,7> is the normal vector

bahrom7893
 2 years ago
Best ResponseYou've already chosen the best response.0Zarkon to the rescue!!!!

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Ok, got that. For the other then, it must be 4,6,14?

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0So from this, how would I determine the answer? Or do I need more?

LagrangeSon678
 2 years ago
Best ResponseYou've already chosen the best response.2if the planes are parrallel then the cross product of their normal vectors should be 0

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.0two plane are parallel iff their normal vectors are parellel

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0I'll try that cross product thing. Thanks guys. I'lll cry out if I have a problem.

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.0two non zero vectors \(\vec{v}\) and \(\vec{u}\) are parallel iff \(\vec{v}=c\vec{u}\) for some scalar \(c\)

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.0is one of the vectors a constant multiple of the other?

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0The first one, multiplied by 2, equals the second one.

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.0if you have the equations 2x+4y7z2=0 4x+6y14z8=0 then you have the normal vectors <2,4,7> and <4,6,14> are these constant multiples of each other?

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0That 4y was suppose to be a 3y....

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0I did mistype that. No wonder my confusion. And probably yours...

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.0then <4,6,14>=2<2,3,7> and so they are parallel...and therefore their planes are parallel

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Awesome. Thank you. This was relatively simple after all...
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