## IsTim 3 years ago Which pairs of planes are parallel and distinct and which are conincident? 2x+4y-7z-2=0 4x+6y-14z-8=0

1. 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.

2. IsTim

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

3. IsTim

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

4. 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?

5. bahrom7893

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

@amistre64 @satellite73 @myininaya

7. bahrom7893

@LagrangeSon678

8. IsTim

Wait. Maybe I'll try something out here.

9. Zarkon

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

10. IsTim

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

11. Zarkon

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

12. Zarkon

<2,4,-7>

13. bahrom7893

Zarkon to the rescue!!!!

14. IsTim

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

15. Zarkon

yes

16. IsTim

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

17. LagrangeSon678

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

18. Zarkon

two plane are parallel iff their normal vectors are parellel

19. IsTim

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

20. Zarkon

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

21. IsTim

Pardon?

22. Zarkon

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

23. IsTim

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

24. Zarkon

really?

25. IsTim

IT seemed so...

26. 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?

27. IsTim

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

28. IsTim

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

29. Zarkon

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

30. IsTim

And distinct??

31. Zarkon

yes

32. IsTim

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