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

Question

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

tkhunny · Answer

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

anonymous · Answer

@tkhunny and then ??

tkhunny · Answer

What do you get?

anonymous · Answer

x=4+5z

tkhunny · Answer

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

anonymous · Answer

Yes i did

anonymous · Answer

Then i did elimination to get rid of y

tkhunny · Answer

Why?  Are they parallel?

anonymous · Answer

Yes

anonymous · Answer

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

tkhunny · Answer

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

anonymous · Answer

its given in the question

tkhunny · Answer

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

anonymous · Answer

so they're not parallel, they intersect ?

tkhunny · Answer

That's what they look like to me.

anonymous · Answer

Answer key says parallel and coincident

tkhunny · Answer

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.