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

1. IsTim Group Title

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.

2. IsTim Group Title

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

3. IsTim Group Title

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

4. IsTim Group Title

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?

5. bahrom7893 Group Title

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

6. bahrom7893 Group Title

@amistre64 @satellite73 @myininaya

7. bahrom7893 Group Title

@LagrangeSon678

8. IsTim Group Title

Wait. Maybe I'll try something out here.

9. Zarkon Group Title

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

10. IsTim Group Title

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

11. Zarkon Group Title

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

12. Zarkon Group Title

<2,4,-7>

13. bahrom7893 Group Title

Zarkon to the rescue!!!!

14. IsTim Group Title

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

15. Zarkon Group Title

yes

16. IsTim Group Title

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

17. LagrangeSon678 Group Title

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

18. Zarkon Group Title

two plane are parallel iff their normal vectors are parellel

19. IsTim Group Title

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

20. Zarkon Group Title

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

21. IsTim Group Title

Pardon?

22. Zarkon Group Title

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

23. IsTim Group Title

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

24. Zarkon Group Title

really?

25. IsTim Group Title

IT seemed so...

26. Zarkon Group Title

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?

27. IsTim Group Title

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

28. IsTim Group Title

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

29. Zarkon Group Title

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

30. IsTim Group Title

And distinct??

31. Zarkon Group Title

yes

32. IsTim Group Title

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