Parametric equations for the line of intersection of two planes (KristaKingMath)

Learn how to find parametric equations that define the line of intersection of two planes.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[samgoddam]

why are we allowed to set z=0 what if that line does not cross z=0 how do we know it does?

[danfoley]

Thank you for all of your videos. I have watched them all from calc 1 and now going through calc 3!

[aryanr]

Explains just like the textbook, good job

[benjaminkrider]

Thank you, this was very helpful. I've watched a few other videos and wasn't able to figure it out until this one.

[maxcepeda]

At @7:00 she uses the vector equation of a line (r = r_naught + tv) where v is the parallel vector (cross product of the normals)

[Ariana-eytg]

oh my god you saved my life! i have a final tomorrow and I had no clue how to do this problem on my practice exam!

[eng-firas]

I'm with you from long time ago and Thanks for all your help.

[shawnscientifica]

Your voice is so ASMR. Will listen to this before bed <3

[HopenGagleMusic]

I am confused why taking the coefficients of the plane gives you a normal vector- I thought normal vectors are derived by taking the cross product...
Any help would be appreciated!

[wilbertcoandadiputra]

thank you, it was really helpful for me in my linear algebra courses

[Persian]

but my problem doesn''t give me zero in its dot product so i ended up to have both number and a coefficeent with t my cross product is (-10, 5, -1) whic ended up with something like I dont know what to do using matrices are much easier.

[TechnoTuner]

After 7 year, watching your video from India 🇮🇳

[jinkypatolay]

Why z is the only variable you subtituted 0? How are the other variabales?

[clarks.]

What do you do if the values of the components are large number like the (1, 0, 0) you got are numbers such as (-10, 14, 0) ....help please

[MShazarul]

Could have explained why we cross product the two normal vector. (If relevant, the cross product results in a third vector that is parallel to the line of intersection) - Took me awhile to understand why we needed to cross product.

[lszbemq]

Hi! If i set y = 0, and solving x+z =1 and x+2z =1 simultaneously, will that change my final answer? Thanks

[omegapolar]

I just do not understand, why we set z=0? Are we allowed to set y or x equal to zero?

[muthapucca]

what happens if one of the intersecting planes is z=0? What would I have to do? I can only find the normal vectors so far, but I don't know how to combine the equations.

[advanstraeten]

Hi Krista, I really really like your explanations on all these subjects I have seen yet. They are clear, have a good tempo, and no distractions ( stuttering and so on;)! Great, and it gives me great pleasure for three years since I am studying Calculus, and I am combining your lessons with information from other sources.
In this 34th lecture in Calc 3 with respect to vectors I am able to follow the algebra. What I don't understand is the underlying concept- really my own problem, I am not that bright when it comes down on 3-D: we have 2 planes, and we find the normal to both. Then I see - if I am right- that by taking the cross product of these normals, we have a line perpendicular to both lines, and so ( is this right?) parallel to both planes?
If my understanding would be correct, what would be the meaning of this parametric equation?
This would be one of your explanations where I could follow most of it, but where I missed the point, you know, to really understand.
By the way, I think you have done a great job explaining all these different subjects in such precise way: great expertise, great teacher, great joy!
Thanks!

[anastasiaanautodidact]

You won't believe how much you're helping us... 😭😭😭😭😭😭😭😭😭