How To Find The Equation of a Plane Given Three Points
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- Опубліковано 4 гру 2019
- This Calculus 3 video tutorial explains how to find the equation of a plane given three points.
Area - Vector Cross Product: • Area of a Parallelogra...
Triple Scalar Product:
• Volume of a Parallelep...
Vector Equations of Lines:
• How To Find The Vector...
The Equation of a Plane:
• How To Find The Equati...
Planar Equation - 3 Points:
• How To Find The Equati...
_______________________________
Lines & Planes - Intersection:
• How To Find The Point ...
Angle Between Two Planes:
• How To Find The Angle ...
Distance Between Point and Plane:
• How To Find The Distan...
Chain Rule - Partial Derivatives:
• Chain Rule With Partia...
Implicit Partial Differentiation:
• Implicit Differentiati...
________________________________
Directional Derivatives:
• How To Find The Direct...
Limits of Multivariable Functions:
• Limits of Multivariabl...
Double Integrals:
• Double Integrals
Local Extrema & Critical Points:
• Local Extrema, Critica...
Absolute Extrema - Max & Min:
• Absolute Maximum and M...
________________________________
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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 UA-cam TV with the 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!
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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
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Do you have to use vectors PQ and PR or could you use vectors PQ and QR
Very good explanation sir.👍
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My final included this one as the first question. But you really need to do saddle pt, and strokes theorem
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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?
Very helpful, Thanks alot
Wow, amazing! Thank you so much!
This video literally helped me in today's test
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)
thank you master for this way to solution
keep going on
Clear explanation thank u
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
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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
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2021 & still helping us all
10Q very much I have understood after several time of my try!
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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
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Thank you so much. This was very easy to follow!!
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!!!
Putting this on 2x speed and it's still easier to keep up with than my instructor
Can u plz make a vdo on vector function and space curve?? Thnks
thank you ♥️
Thank you soo much 🙂
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.
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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
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
Instead of doing PR and PQ could you do QR and QP? Like why did we use P in that position
explain me the last part where yyou stated a new equation(which is equal to 0)
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Why is it "-" in the determinant of the matrix operation in the first ? 3:02?
PLEASE
THANK U
how do you know if the three points are collinear from this equation?
What if the question is exactly this but also with z=0 and time t=0 specified?
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.
Can you help me with this ? If point P is considered the coordinate origin (0,0) inside the plane, and I have a point (t, u) on the plane, how can I map that to 3d coordinates using the equation ?
do you have to use point p? or can it be any point
Any point should work.
Any points will work 😇
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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
Awesome!!
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
how to calculate using plane equation to find roll pitch yaw angles
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This video literally saved me from a quiz
can we use any point as my point P would be (0,0,0)
After obtaining the normal vector, we can use any point included in the problem?
yes
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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
wait i dont get it, why was point P's coordinates specifically used in the calculation of the plane equation. Can point Q and R be used also?
yes, it doesn't matter which point that u use you can use point Q and R and still get the same result
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
Easier done than said becsuse of this man
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.
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Bro, a minute into your video and I understand more than the hours I’ve spent in lectures