Parametric equations for the line of intersection of two planes (KristaKingMath)
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- Опубликовано: 25 авг 2024
- ► My Vectors course: www.kristaking...
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?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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This woman have save lives! Thanks!
Thank you for all of your videos. I have watched them all from calc 1 and now going through calc 3!
Wow, that's awesome! I'm so honored, thank you so much for watching! :D
How's it going now bro?
Thank you, this was very helpful. I've watched a few other videos and wasn't able to figure it out until this one.
Oh good! I'm so glad it helped! :D
Explains just like the textbook, good job
Thank you so much! 😊
I'm with you from long time ago and Thanks for all your help.
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!
why are we allowed to set z=0 what if that line does not cross z=0 how do we know it does?
Damn, 2 years and nobody replied to this dude
feels bad
Any plane with normal vector not perpendicular to a vector lying in the xy plane would cross the xy plane
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
Don’t question bruv just go with the flow..
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)
Your voice is so ASMR. Will listen to this before bed
You sick fuck (I will too)
thank you, it was really helpful for me in my linear algebra courses
After 7 year, watching your video from India 🇮🇳
best explanation so far, thanks!
Thank you. You are very helpful!
Saved my 2018 Spring semester and now saving my Calc 3 Summer semester.
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!
idk bruh
Perfect, my only thought was you should have explained the vector equation formula, r(t)=r_intial +t(v)
Why z is the only variable you subtituted 0? How are the other variabales?
But thanks for this it helps a lot but I still confuse with that 0
very very great video.
thank you so much
+Chew Vincent You're welcome, I'm so glad it helped!
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.
You won't believe how much you're helping us... 😭😭😭😭😭😭😭😭😭
I'm so glad I'm able to help, Anastasia! :)
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
Your videos are very much appreciated!
:)
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.
Hi! If i set y = 0, and solving x+z =1 and x+2z =1 simultaneously, will that change my final answer? Thanks
No
i got a hundred on my assignment thank you 😃😃
Awesome!!! You helped me a lot! Thank you so much!
+Max Johnson You're welcome, I'm so glad it helped!
You should illustrate using pictures so that people would get a sense for why they are using these methods you are teaching.
why we need to take cross product
excellent!
Thanks, Michael! :)
the lone constant on the ohter side of the equals sign doesn't matter until after finding the cross product right?
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?
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.
I think you need to take off the subtitles on RUclips, that way you'll be able to see what's behind them. :)
Thank you !!!
You're welcome, Haja! :)
well done,thank you to help me
Great video. Gave it a thumbs up.
+Tanner M Thank you so much!
Why do you set z=0?
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.
Thank you very much
You're welcome! :)
Why use cosine of theta to find the angle of intersection instead of sine of theta?
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
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!
Thank you
you're welcome!
woow ur videos is so useful thank you
+my-tv nice You're welcome!
You are my knight in shining armor...thank you so much!
+Sharingan1997x You're welcome!
Thank you so much!!!
You're welcome, Sara! :)
Good
Thanks! :)
my problem the equations are not both = 1. they're completely different and setting x to 0 doesn't help me
what if you have the intersection line but not the two planes an du need to find the two planes?
Whats the logic when we put z=0?? Can u put y=0 instead of z?
I just do not understand, why we set z=0? Are we allowed to set y or x equal to zero?
Can we make x or y zero in place of z to find the point?
why do we need to do the cross product? whats the relevance of it please? thanx.
this cleared up alot for me, thank you very much
@@madeleinejansson4278 thanks so much
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 😂
Thank you very much :)
You're welcome!
Do one with out zeros please
remember that time you used to complain about how hard trig was? now your in calc3, how does it feel slugger?
woww thanks a lot! more videos
You're welcome, I will definitely keep creating more videos! :D
wrt 12:09 => but if arccos(5/sqrt(27)) = 0.275 radians = 15.793 degrees. Why is it wrong to go with radians?
+and then i said not calc
Can i set x or y = 0
what if the line of intersection does not posses through Z=0
nah krista chill you going to crazy bro
linear Algebra is very hard at first to conceptualize...
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 ??
normal means perpendicular
That stuff can be explained in 2 minutes @RiteshReddy
thanks u save my life love u UwU
why z = 0. i also came for x = 0. but for y = 0 it gave math error
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.
why do you need two normal vectors I thought we just need one
Why is Z zero
You are the best woman 👩❤💕💓💗
👍👍👍
1/24/2017
may lord krishna bless you :) thanks for the help
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?
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.
ha, sorry about that! I know it's something I need to work on. 😁
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!
no no we initially set z = 0.. you probably are in PDE now so this comment is useless
You sound like Pam from The Office
:D
degrees are about as useful as an art degree
Hi! If i set y = 0, and solving x+z =1 and x+2z =1 simultaneously, will that change my final answer? Thanks
You can still find your coordinate point by setting x,y, or z equal to 0 ;)