## burhan101 2 years ago Are these planes parallel and distinct or parallel and coincident ? 3x+9y-6z-24=0 4x+6y-14z-8=0

1. tkhunny

Divide the first by 3 and the second by 2, for starters.

2. burhan101

@tkhunny and then ??

3. tkhunny

What do you get?

4. burhan101

x=4+5z

5. tkhunny

?? What is that? I was hoping you would get: x+3y-2z-8=0 2x+3y-7z-4=0

6. burhan101

Yes i did

7. burhan101

Then i did elimination to get rid of y

8. tkhunny

Why? Are they parallel?

9. burhan101

Yes

10. burhan101

We have to figure of if theyre parallel and distinct or coincidentt

11. tkhunny

They are? What makes you think so? When you eliminated y, didn't that give you a line in the x-z plane?

12. burhan101

its given in the question

13. tkhunny

Are you going to buy it, just because it says so? If they are parallel, shouldn't they have the same Normal Vector?

14. burhan101

so they're not parallel, they intersect ?

15. tkhunny

That's what they look like to me.

16. burhan101

Answer key says parallel and coincident

17. tkhunny

3x+9y-6z-24=0 4x+6y-14z-8=0 Find a point on one of them. (10,0,1) Prove 3(10) + 9(0) - 6(1) - 24 = 30 + 0 - 6 - 24 = 24 - 24 = 0 Is it on the other one? 4(10) + 6(0) - 14(1) - 8 = 40 - 14 - 8 = 26 - 8 = 18 \(\ne 0\) Okay, we just proved that they are NOT coincident. Did you write the problem correctly? If you did, we're done.