Thanks to you I might just pass my exam tomorrow... Corona and restructuring made our classes a clusterfuck of doom. You're a savior, even if I don't make it through my exam! UPDATE: Exam passed with margin to spare! THANK YOU!
Professor Organic Chemistry Tutor, thank you for a short and sweet video/lecture on How to Find the Equation of a Plane Given Three Points. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
ive been watching your videos from trig all the way up to where i am now which is calc III i cannot express how thankful i am for you and your videos. !!!!!!!!!THANK YOU ORGANIC CHEMISTRY TUTOR!!!!!!!!!
thank you so much for this!! my math teacher goes through all the steps so fast i can't keep up lol (off topic but i also just saw this vid was posted on my birthday haha). your channel is full of helpful videos! subscribed!
Yall go to Geogebra 3D calculator and put in: a=vector ((0,0,0),(random coords)) b= Same as a but change coords w=cross(a,b) gives you a 3d representation of the cross product and how it shifts the plane.
The matrix will work but you can save a lot of time doing the cross product another way. 1. Put the vectors in the i j k form. 2. Write i, j, k in a clockwise circle. As you go around to the right, i*j=k, j*k=i, k*i=j. ORDER MATTERS, but it works the same way if you go the other way, its just negative. j*i= -k, etc. 3. Multiply them together as you would a regular polynomial (foil) but pull the constant out front and leave the letter terms inside the parenthesis (ex. 3i * 4k = 12 (i*k) = 12(-j). 4. Simplify answer down to the three ijk terms and rewrite vector however you need to.
oooh I found another way to do this! We haven't leant cross product at school yet, but I used the scalar product (same as dot product) to do it. The scalar product of two perpendicular vectors is zero, (because cos 90 is 0), so I set the vector of the normal vector to (n1, n2, n3), and then you can do the scalar product with vector PR and PQ, and set up simultaneous equations. Then u get the ratio of (n1:n2:n3), and only the ratios matter so u can use that as the normal vector. Then just substitute the values we know to find d, and you're done
Thank you! I thought you didnt do multivariable, but I am so pleased to find this. I have only ever passed my northwestern university classes due to your help. when I get out im gonna get paid and send you a large check to aid in your mission! God bless you!!!!
How do you know if we should do PQ x PR or PR x PQ? Because the order of cross product will lead to different answer. And also, do other vectors (facing other direction) work fine as well? For example, QP x RP , or RP x RQ
Is it needed that we use (x - xnaught), (z - znaught), (y - ynaught) when solving for the Cartesian Equation for D? Our teacher teached us that we only sub for x, y, and z the points to solve for D, then we resubmit D into the the equation, and we solved for the Cartesian equation.
Any two vectors would do, because they all lie on the plane. The cross product therefore would always come out the same, so you'll get the same equation for your normal no matter what you choose to use.
yep. by subtracting the vectors we form the two lines that meet at one end. then we find the cross product of them. that's why we took P as the point the lines join at
From the definition of determinants, the sign switches. If you were doing a 5x5 determinant, you'd do +, -, +, -, + along with the resulting 4x4 determinants. For each 4x4, you would do +, -, +, - along with the 3x3 determinants. Then for each 3x3, you would do +, -, + along with the 2x2 determinants. As you can see, this method of computing determinants is very inefficient. There are better ways to do it when it's bigger than 3x3. By the way, notice that the 2x2 determinant is nothing special. you do topleft*det(bottom right) - topright*det(bottom left), which is just topleft*bottomright - topright*bottomleft
Does anyone know what happens if one of your values of x, y or z ==0? Ex. if my final equation is 6y - z = 5, does this just mean the plane is just on the yz axis?
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This man is gettting me though engineering at university 🙌
U have this in university bro we got this and i am still in high school. Shit country i am in😥.
@@bahaknp332 and here I wish i was introduced to this in high school.
@@bahaknp332 india?
same here
Through*
Greatest teacher on RUclips
Thanks to you I might just pass my exam tomorrow... Corona and restructuring made our classes a clusterfuck of doom.
You're a savior, even if I don't make it through my exam!
UPDATE: Exam passed with margin to spare! THANK YOU!
about to do the same!!!!
THANK YOU. YOU HAVE NO IDEA HOW MUCH THIS HELPED.
Professor Organic Chemistry Tutor, thank you for a short and sweet video/lecture on How to Find the Equation of a Plane Given Three Points. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
ive been watching your videos from trig all the way up to where i am now which is calc III i cannot express how thankful i am for you and your videos.
!!!!!!!!!THANK YOU ORGANIC CHEMISTRY TUTOR!!!!!!!!!
I am from Pakistan.. really you are the best teacher in the youtube 💯amazing job.. good luck
thank you so much for this!! my math teacher goes through all the steps so fast i can't keep up lol (off topic but i also just saw this vid was posted on my birthday haha). your channel is full of helpful videos!
subscribed!
Organic Chemistry tutor is my savior
thanks for this....everytime i watched your videos, i would never forget to like and comment..keep up the great work
FIrst video where i actually learned something properly thank you
We can even use a standard formula
x-x1 y-y1 z-z1
x2-x1 y2-y1 z2-z1
x3-x1 y3-y1 z3-z1
Determinant equals to zero
Best teacher on RUclips!
Looking through different sources, none were so clearly explained as this. It really does feel like a private tutor! Thanks a million!
He tells you what to do but doesnt explain the concept behind it. Good enough to find a plane equation I guess...
I was thinking about the same thing! Why did I get the perpendicular vector when I used a x b? Does that always work?
Or why we use that formula in the end. I guess it is derived from the two vectors and point that define the plane?
My favorite teacher in you tube
Yall go to Geogebra 3D calculator and put in:
a=vector ((0,0,0),(random coords))
b= Same as a but change coords
w=cross(a,b)
gives you a 3d representation of the cross product and how it shifts the plane.
The matrix will work but you can save a lot of time doing the cross product another way.
1. Put the vectors in the i j k form.
2. Write i, j, k in a clockwise circle. As you go around to the right, i*j=k, j*k=i, k*i=j. ORDER MATTERS, but it works the same way if you go the other way, its just negative. j*i= -k, etc.
3. Multiply them together as you would a regular polynomial (foil) but pull the constant out front and leave the letter terms inside the parenthesis (ex. 3i * 4k = 12 (i*k) = 12(-j).
4. Simplify answer down to the three ijk terms and rewrite vector however you need to.
you are the best. the picture at the beginning helped immensely
This is a world guineas record explanation 🎉🎉🎉❤
My man is on it again...Always the best explanation of contents❤
THANK YOU SOOO MUCH YOU DO NOT UNDERSTAND HOW MUCH YOU HELPED ME 😭😭
Greatest teacher, thx
i dont know what to say your are savior thank you man !!!!
Thank you so much I appreciate your work for us
My final included this one as the first question. But you really need to do saddle pt, and strokes theorem
Always delivers up to expectations.
oooh I found another way to do this! We haven't leant cross product at school yet, but I used the scalar product (same as dot product) to do it. The scalar product of two perpendicular vectors is zero, (because cos 90 is 0), so I set the vector of the normal vector to (n1, n2, n3), and then you can do the scalar product with vector PR and PQ, and set up simultaneous equations. Then u get the ratio of (n1:n2:n3), and only the ratios matter so u can use that as the normal vector. Then just substitute the values we know to find d, and you're done
we don't do vector product at edexcel so the way you did it can you explain it simply i am having hard time following this
thank you
Thanks manhhh(really helped in assignment)
Thank you! I thought you didnt do multivariable, but I am so pleased to find this. I have only ever passed my northwestern university classes due to your help. when I get out im gonna get paid and send you a large check to aid in your mission! God bless you!!!!
This video literally helped me in today's test
Very good explanation sir.👍
Excellent professor, telling all the necessary in compact ways, giving us time to make notes. That's what we need!
Putting this on 2x speed and it's still easier to keep up with than my instructor
Bro if I get rich someday I will share some money with you.
Why was the sign in front of the j coefficient a negative?
signs alternate whenever you expand a matrix (a11 is +, a12 is - and so on)
@@stoppls1709 Thank you! Had the exact same question!
You are the greatest thing to happen to Earth.
You are life saver thank you so much
your videos are soo helpful. thanks alot
your are useful person in the RUclips
Thank you so , much u explain this so easily, helped a lot.
I love this man 💙
Thank you Sir
Thank you so much sir....Your example hlep me a lot ❤️
How do you know if we should do PQ x PR or PR x PQ? Because the order of cross product will lead to different answer. And also, do other vectors (facing other direction) work fine as well? For example, QP x RP , or RP x RQ
Take the first point as the a vector and the other as b or in simple words , what comes first will be a and the other will be b
10Q very much I have understood after several time of my try!
Thanks so much - very helpful!
Is it needed that we use (x - xnaught), (z - znaught), (y - ynaught) when solving for the Cartesian Equation for D? Our teacher teached us that we only sub for x, y, and z the points to solve for D, then we resubmit D into the the equation, and we solved for the Cartesian equation.
both works, pick whichever method you prefer or find easier!
thank you master for this way to solution
keep going on
This video literally saved me from a quiz
We getting out the exam with this one
2021 & still helping us all
Wow, amazing! Thank you so much!
i'd throw all my tuition to this guy instead of my profs
Thank you ❤️❤️
Very helpful, Thanks alot
Why is it "-" in the determinant of the matrix operation in the first ? 3:02?
PLEASE
The G.o.a.t like Lionel Messi 💕
thank you sir, you're the besttt 🥰
Do you have to use vectors PQ and PR or could you use vectors PQ and QR
Any two vectors would do, because they all lie on the plane. The cross product therefore would always come out the same, so you'll get the same equation for your normal no matter what you choose to use.
how do you know which vectors subtract form which vectors? does it matter?
yep. by subtracting the vectors we form the two lines that meet at one end. then we find the cross product of them. that's why we took P as the point the lines join at
Zor jwana bram bzhit bardawam ba
Clear explanation thank u
why in 5:26 we take point p or doesnt it matter which point to take?
Take the point that is a part of both of the vectors that you used in the cross product (in this case, PR and PQ)
@@tomc53 It actually doesn't matter which point you take as long as it's on the plane.P,Q,R are all valid.
You good dawg
very useful thank you so much
Can u plz make a vdo on vector function and space curve?? Thnks
anyone watching in 2024
Here
here
Bruh im literally using this to pass my calculus exams
Yhh. But his approach is different from what we were thought in class so I'm not going by this
Hi
Thanks buddy
I'm curious, why is the determinant of j subtracted instead of added?
I want to know as well.
Exactly, I had to scroll to see if someone noticed. It should be a mistake from his side
you are amazing!
Instead of doing PR and PQ could you do QR and QP? Like why did we use P in that position
Why did you minus j from i when setting up the cross vectors
From the definition of determinants, the sign switches. If you were doing a 5x5 determinant, you'd do +, -, +, -, + along with the resulting 4x4 determinants. For each 4x4, you would do +, -, +, - along with the 3x3 determinants. Then for each 3x3, you would do +, -, + along with the 2x2 determinants. As you can see, this method of computing determinants is very inefficient. There are better ways to do it when it's bigger than 3x3.
By the way, notice that the 2x2 determinant is nothing special. you do topleft*det(bottom right) - topright*det(bottom left), which is just topleft*bottomright - topright*bottomleft
you saved my head
This man almost at 3 mil
Anyone watching from The University of Zambia
Here.Lol😅
@@Noble-r2e Engineering math innit? 😭
hello i have a question why does in 3:17 the k need to be plus or i to j need to be minus, thankyou
Thank you so much, well explained.
do you have to use point p? or can it be any point
Any point should work.
Any points will work 😇
Does anyone know what happens if one of your values of x, y or z ==0? Ex. if my final equation is 6y - z = 5, does this just mean the plane is just on the yz axis?
Yeah
Thank you soo much 🙂
thanks bro!
why P is the initial point? Could it be a different point like R or Q ?
Yaa im curious also
yes, it doesnt matter you will get same result
You are my favorite.
What if the question is exactly this but also with z=0 and time t=0 specified?
Thank you !
thank you ♥️
explain me the last part where yyou stated a new equation(which is equal to 0)
thank you man
After obtaining the normal vector, we can use any point included in the problem?
yes
3:10 why did we do - then plus?
Easier done than said becsuse of this man
Thank you so much. This was very easy to follow!!
Thank you for making these amazing videos!
you are doing god's work
how do you know if the three points are collinear from this equation?
Thank you!!!
Saved me again
how to calculate using plane equation to find roll pitch yaw angles
can we use any point as my point P would be (0,0,0)
I'm studying this for my college entrance exam in india 🙂🤝