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

[@aryanr1681]

Explains just like the textbook, good job

[@kristakingmath]

Thank you so much! 😊

[@eliecerecology]

This woman have save lives! Thanks!

[@danfoley1604]

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

[@kristakingmath]

Wow, that's awesome! I'm so honored, thank you so much for watching! :D

[@lolnou2291]

How's it going now bro?

[@benjaminkrider7173]

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

[@kristakingmath]

Oh good! I'm so glad it helped! :D

[@samgoddam]

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

[@matheusflx1]

Damn, 2 years and nobody replied to this dude

[@nestorlopez4284]

feels bad

[@carloscerritoslira328]

Any plane with normal vector not perpendicular to a vector lying in the xy plane would cross the xy plane

[@matthewaskar9559]

so i think its because in order to find a point you can set any variable to zero, so in her case she just set z=0 and just use that to find a point

[@stealthninja63]

Don’t question bruv just go with the flow..

[@maxcepeda5571]

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)

[@eng-firas5358]

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

[@Ariana-ey9tg]

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!

[@TechnoTuner]

After 7 year, watching your video from India 🇮🇳

[@shawnscientifica6689]

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

[@MegaLoquendo2000]

You sick fuck (I will too)

[@anastasiaanautodidact9856]

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

[@kristakingmath]

I'm so glad I'm able to help, Anastasia! :)

[@wilbertcoandadiputra2487]

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

[@wazzupweek]

best explanation so far, thanks!

[@advanstraeten2841]

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!

[@davidwangg]

idk bruh

[@haqinc]

Perfect, my only thought was you should have explained the vector equation formula, r(t)=r_intial +t(v)

[@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.

[@Mericali916]

Saved my 2018 Spring semester and now saving my Calc 3 Summer semester.

[@amoszegrkaar]

I love the display, it is more clearer with full understanding. But the type writings has covered the steps till the end. Can you remove the type writings and display the steps in full for this particular lesson. I was following to a stage and I can't see anything again.

[@kristakingmath]

I think you need to take off the subtitles on KZbin, that way you'll be able to see what's behind them. :)

[@bestyoueverhad.2408]

Hi. say instead of zeros on your co-ordinate points how do you then go about getting a nicely tidied up solution, because your example works out hassle free. Thanx

[@TheMadIrishDev]

Thankyou!

[@janetsanders9523]

Hi. I have watched a few of your videos, and I wanted to tell you that you are saying "discriminant" when you mean "determinant". Thanks for your good explanations!

[@sevakminasyan1554]

Thank you. You are very helpful!

[@menahasan5718]

i got a hundred on my assignment thank you 😃😃

[@ashishkadari-ol8jn]

THANK YOU SO MUCH

[@mikam.5156]

Your videos are very much appreciated!

[@kristakingmath]

:)

[@Netharino]

very very great video. thank you so much

[@kristakingmath]

+Chew Vincent You're welcome, I'm so glad it helped!

[@jinkypatolay628]

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

[@jinkypatolay628]

But thanks for this it helps a lot but I still confuse with that 0

[@Persian771]

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 -18+(-10)t)i+(12+5t)j+(0+(-1)t)k I dont know what to do using matrices are much easier.

[@RennatWebs]

Great video. Gave it a thumbs up.

[@kristakingmath]

+Tanner M Thank you so much!

[@MayelGura]

You should illustrate using pictures so that people would get a sense for why they are using these methods you are teaching.

[@dudeinspace1491]

Whats the logic when we put z=0?? Can u put y=0 instead of z?

[@TheJudoJoker]

the lone constant on the ohter side of the equals sign doesn't matter until after finding the cross product right?

[@muthapucca2502]

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.

[@maxjohnson5585]

Awesome!!! You helped me a lot! Thank you so much!

[@kristakingmath]

+Max Johnson You're welcome, I'm so glad it helped!

[@babali7588]

It's not okay to put a zero on the Z. It does not matter for a classic exam but when we are responsible of the test exam that's matter because. Z=0 and Y=0 are not give the same answer. Am i wrong?

[@imangjamatia2693]

Can we make x or y zero in place of z to find the point?

[@clarks.5428]

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

[@allistermi6014]

why we need to take cross product

[@980ad5]

Thank you !!!

[@kristakingmath]

You're welcome, Haja! :)

[@schrodingerscat3912]

remember that time you used to complain about how hard trig was? now your in calc3, how does it feel slugger?

[@pacifiquensabimana3838]

well done,thank you to help me

[@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!

[@MikhailJones-s5c]

If you're given a point, (x0,y0,z0), in the plane, and a normal vector, n=, that is orthogonal to the plane, then any other point (x,y,z) will be in the plane if and only if the vector between (x0,y0,z0) and (x,y,z) is orthogonal to . I.e., their dot product is 0. That gives you the equation: dot=0 that is, a(x-x0)+b(y-y0)+c(z-z0)=0 The equation of the plane is based on the principle of being the dot product of the orthogonal vector (the coefficients) and equaling 0, but even if the d in the equation of a plane isnt equal to 0, the coefficients will still apply because they are going to be parallel to the vector orthogonal (and thus orthogonal themselves)

[@my-tvnice2696]

woow ur videos is so useful thank you

[@kristakingmath]

+my-tv nice You're welcome!

[@عليرمضانكاطع-ث2ض]

Thank you very much

[@kristakingmath]

You're welcome! :)

[@HassanMohd]

Why use cosine of theta to find the angle of intersection instead of sine of theta?

[@cashtupe9565]

why do we need to do the cross product? whats the relevance of it please? thanx.

[@2011maverickschamps]

this cleared up alot for me, thank you very much

[@patricksweet6121]

@@madeleinejansson4278 thanks so much

[@michaeltheisen]

excellent!

[@kristakingmath]

Thanks, Michael! :)

[@omegapolar1355]

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

[@areebanwar9229]

what if you have the intersection line but not the two planes an du need to find the two planes?

[@apple3033]

You showed how to do it but I don’t really understand why this works.

[@Sharingan1997x]

You are my knight in shining armor...thank you so much!

[@kristakingmath]

+Sharingan1997x You're welcome!

[@Zeppelinpuppy]

Thank you

[@kristakingmath]

you're welcome!

[@EddTerranGe]

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

[@フアン-f6e]

You can still find your coordinate point by setting x,y, or z equal to 0 ;)

[@alfonshomac]

wrt 12:09 => but if arccos(5/sqrt(27)) = 0.275 radians = 15.793 degrees. Why is it wrong to go with radians?

[@Alphasone0212]

+and then i said not calc

[@esiasonR77]

Do one with out zeros please

[@saramoussakone5190]

Thank you so much!!!

[@kristakingmath]

You're welcome, Sara! :)

[@quantaali543]

what if the line of intersection does not posses through Z=0

[@strugglingcollegestudent]

my problem the equations are not both = 1. they're completely different and setting x to 0 doesn't help me

[@danny_not_young]

Thank you very much :)

[@kristakingmath]

You're welcome!

[@tisztaa]

Why do you set z=0?

[@arjunsatwani9664]

That stuff can be explained in 2 minutes @RiteshReddy

[@habbggj4854]

Please try to answer me .. for equation of line we need to .. point .. and normal(parallel) vector .. but here .. we got a perpendicular vector n point ??

[@leeostadi7900]

normal means perpendicular

[@richardakrong5590]

woww thanks a lot! more videos

[@kristakingmath]

You're welcome, I will definitely keep creating more videos! :D

[@ferdinandndaka2357]

Good

[@kristakingmath]

Thanks! :)

[@iooioo553]

Can i set x or y = 0

[@instaminox]

linear Algebra is very hard at first to conceptualize...

[@bogha]

nah krista chill you going to crazy bro

[@kevinlimapena5698]

thanks u save my life love u UwU

[@lschan9242]

you will find this video helpful when your lecturer didn't teach you this topic bt insists u to do the tutorial on this topic 😂

[@krishanudev7573]

may lord krishna bless you :) thanks for the help

[@2011maverickschamps]

why do you need two normal vectors I thought we just need one

[@slingshot7602]

why z = 0. i also came for x = 0. but for y = 0 it gave math error

[@anwarulbashirshuaib5673]

You need to find any point on the line of intersection. Suppose, such a point is (x,y,z). Since you have the freedom to pick any point, you can set either of x or y or z to any value you like and solve the other two from the equations of those planes. For example, you could set z=10 and solve for x,y. Or you can set y=5 and solve for x,z, and so on. However for this specific problem, you don't have the freedom to choose x=something which I explained below: If you put x=0, then you get: y+z = 1 2y+2z = 1 There are no solutions for this system of equations. This is because there are no points on the line of intersection (LOI) with x=0. The direction vector of the LOI is which is parallel to the yz plane. So there is only one value for x which this LOI passes through, and using only that value would give you a solution for y,z. To get around this, just set y=something or z=something instead of x.

[@SexualPotatoes]

Great video. Please watch the handwriting - your 2 looks too much like a z, and your t looks too much like +. It was very confusing.

[@kristakingmath]

ha, sorry about that! I know it's something I need to work on. 😁

[@godsonfialor5014]

Why is Z zero

[@TemamShibiru-mc7tf]

You are the best woman 👩❤💕💓💗

[@erdemalpkaya]

I cannot understand all this solution find just this (-)* x+y+z=1 x+2y+2z=1 ------------------------ y+z=0 so z=-y then if z=t y = -t and we found x=1!

[@schrodingerscat3912]

no no we initially set z = 0.. you probably are in PDE now so this comment is useless

[@benjaminfikhman370]

You sound like Pam from The Office

[@kbqz]

Nobody on the whole youtube know how to find the intersection of two planes when you have their parametric equation without changing the equation and keeping it parametric. I know how to do it but the method is very long, nobody has a alternative /fastest method?

[@wangchul]

1/24/2017

[@MrMossadiq]

👍👍👍

[@mustafabannan5371]

:D

[@icelick6912]

degrees are about as useful as an art degree

[@方志伟-n9m]

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

[@cuneiformed]

No