IsTim
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
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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
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I managed to answer some unrelated questions beforehand, but I don't know how I managed to solve them...
IsTim
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So I figured out the normals were [2,3,7] and [4,6,-14]
IsTim
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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
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that should be parallel and distinct.. if u can just multiply them by a scalar, but i suck at this, so idk.. @Mertsj @Zarkon
bahrom7893
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@amistre64 @satellite73 @myininaya
bahrom7893
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@LagrangeSon678
IsTim
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Wait. Maybe I'll try something out here.
Zarkon
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how is [2,3,7] the normal vector?
IsTim
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Er, I just looked at my notes and inferred that...
Zarkon
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if 2x+4y-7z-2=0 is your equation then <2,4,7> is the normal vector
Zarkon
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<2,4,-7>
bahrom7893
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Zarkon to the rescue!!!!
IsTim
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Ok, got that. For the other then, it must be 4,6,-14?
Zarkon
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yes
IsTim
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So from this, how would I determine the answer? Or do I need more?
LagrangeSon678
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if the planes are parrallel then the cross product of their normal vectors should be 0
Zarkon
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two plane are parallel iff their normal vectors are parellel
IsTim
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I'll try that cross product thing. Thanks guys. I'lll cry out if I have a problem.
Zarkon
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two non zero vectors \(\vec{v}\) and \(\vec{u}\) are parallel iff \(\vec{v}=c\vec{u}\) for some scalar \(c\)
IsTim
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Pardon?
Zarkon
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is one of the vectors a constant multiple of the other?
IsTim
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The first one, multiplied by 2, equals the second one.
Zarkon
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really?
IsTim
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IT seemed so...
Zarkon
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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
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That 4y was suppose to be a 3y....
IsTim
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I did mistype that. No wonder my confusion. And probably yours...
Zarkon
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then <4,6,-14>=2<2,3,-7>
and so they are parallel...and therefore their planes are parallel
IsTim
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And distinct??
Zarkon
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yes
IsTim
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Awesome. Thank you. This was relatively simple after all...