Question

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

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

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?

Answer 5

that should be parallel and distinct.. if u can just multiply them by a scalar, but i suck at this, so idk.. @Mertsj @Zarkon

Answer 6

@amistre64 @satellite73 @myininaya

Answer 7

@LagrangeSon678

Answer 8

Wait. Maybe I'll try something out here.

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

<2,4,-7>

Answer 13

Zarkon to the rescue!!!!

Answer 14

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

Answer 15

yes

Answer 16

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

Answer 17

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

Answer 18

two plane are parallel iff their normal vectors are parellel

Answer 19

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

Answer 20

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

Answer 21

Pardon?

Answer 22

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

Answer 23

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

Answer 24

really?

Answer 25

IT seemed so...

Answer 26

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?

Answer 27

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

Answer 28

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

Answer 29

then <4,6,-14>=2<2,3,-7>

and so they are parallel...and therefore their planes are parallel

Answer 30

And distinct??

Answer 31

yes

Answer 32

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