It's very neat how we start by defining a P0 and it then disappears leaving just the components of P1 in the final formula. What a plot twist! Nice video - thanks.
Professor Organic Chemistry Tutor, thank you for deriving the mathematical formula that is used to Find the Distance Between a Point and a Plane. Deriving formulas in Mathematics increases my knowledge/understanding of the material. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
The way I can understand concepts by watching your video always amazes me. Because I understand the math but no the concept with my professors and I just need to watch your videos and I'm all set. THANK YOU!
3:14 why did you have to do the projection stuff instead of forming the triangle between points p0, p1, and the point where D touches the plane? And then you can get the trig identity costheta = D/|B| and then rearrange for D= costheta*|B|? What was the purpose of the scalar projection of B onto N?
Concretely, I think the reason why ax0+by0+cz0 replace by ax+by+cz is because P0 is in the plane ax+by+cz=-d, thus they are equal to each other. btw, insightful explanation.
I was taught with a positive d on the right side because it doesn’t matter. You just replace the form ax+by+cz with whatever is on the right and don’t have to worry about 2 sign changes.
Alternatively you can think any point on the plane satisfies ax + by + cz = 10 so you can replace the second grouping corresponding to the point on the plane with 10 so you don’t get confused by the sign of d.
Hey Dude, your explanation is amazing. I want to ask, how to find the closest point from a point to a plane or line. If you've explained it in another video, please let me know. thank you
00:02:25 where he says "D is the absolute value of the scalar projection..." he writes "D = comp n B" on the blackboard. I'm not sure what that means exactly or did I misread what he wrote. Anyone have any idea?
So, if you dot B and n, you'll get the projection of B onto n (which is basically what dot product is). But, if you see carefully, the projection B makes on n is equal to the distance D. That's why he wrote D = comp of B on n
Why are we considering the plane 6x- 3y+2z= 10 to be equal to n vector instead of the horizontal plane perpendicular to point p as depicted in the video?
Why not just find the line equation (we have direction and position vectors already)? We then substitute x, y and z of the line into the plane equation and solve for the paramater. We then obtain the parameter that we can use to calcualate the point that lies on both plane and the line (which means exactly under the point we are looking for). Then simply calculate the distance between two points and we have the solution.
Does anyone know if he does statistics videos? He helped me get an A in algebra1 and an A in algebra2. Now onto stats next semester which I haven't a clue what I will be learning 🤯
I wish I had just followed your videos and not spent weeks trying to decipher our damn textbook, written by a mathematician, for mathematicians... not for students.
What happens if the point is not perpendicular to the plane ? Would you still be able to use the scalar projection of b onto n to find D (the distance)?? Anybody know ???
The distance of a point n with coordinates (a, b, c) from origin is denoted by |n| and is equal to sqrt(a^2 + b^2 + c^2). This is from the equation of distance between two points and substitute the second point as origin i.e (0, 0, 0)
Oh, okay thank you so much, so he substituted the n in, so we have to generally know this square root part or do you know how it was derived, i don't want to confuse but would it be from the a^2+b^2=c^2 formula? Thanks
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It's really helpful when you go back and explain where the formula come from, rather than just use them. Thank you
i feel like this guy will go straight to the heaven just because the number of engineers he molded
Engineers, math students, science students, and even highschool students...he'd literally be in the highest level of heaven
yup, not only his contry's but worldwide
@@مريَم-ط5م7غ insha Allah he will be. May God make his life easy, and give him a courage to stand against hard times. Ameen.
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Took my general chem 1 ACS today and got an 82 without your videos I don’t think that would’ve been possible without your help. Thank you sooo much!!!
You got an 82 without his videos? Or maybe 2 sentences?
bro said WITHOUT your vids and then went on to score 82 and THEN BRO SAYS THAT HE HELPED HIM
Is bro HIGH??
really love your videos, they've helped me a lot in understanding my compacted ap calc class, keep up the good videos!
Jacob Hellenbrand yesterday was my test this dude just saved my head
This just helped me solve a problem I had spent 4 hours on. Your vids are Khan academy level or better! Thanks!
It's very neat how we start by defining a P0 and it then disappears leaving just the components of P1 in the final formula. What a plot twist! Nice video - thanks.
Professor Organic Chemistry Tutor, thank you for deriving the mathematical formula that is used to Find the Distance Between a Point and a Plane. Deriving formulas in Mathematics increases my knowledge/understanding of the material. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
The way I can understand concepts by watching your video always amazes me. Because I understand the math but no the concept with my professors and I just need to watch your videos and I'm all set. THANK YOU!
love how straight to the point the video thumbnail is
From the bottom of my heart.. I owe you my life
His voice... Is the most soothing
ur so helpfull and determined
God bless you
thanks for the video! it has helped me through so many difference topics (differentiation, integration, laplace trans, matrix, vectors etc)
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Learning Soo much from your channel
Thank You Unknown Sir
Thank you very much for showing us the easiest way we can solve such these problems
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3:14 why did you have to do the projection stuff instead of forming the triangle between points p0, p1, and the point where D touches the plane? And then you can get the trig identity costheta = D/|B| and then rearrange for D= costheta*|B|? What was the purpose of the scalar projection of B onto N?
Awesome explanation
This guy is top G. I might pass cuz of this dude.
you always save my life
IAppreciate all your videos sir
dude, you're genius 😎
I love you ochem tutor. I will die for you
Concretely, I think the reason why ax0+by0+cz0 replace by ax+by+cz is because P0 is in the plane ax+by+cz=-d, thus they are equal to each other.
btw, insightful explanation.
I was taught with a positive d on the right side because it doesn’t matter. You just replace the form ax+by+cz with whatever is on the right and don’t have to worry about 2 sign changes.
Thank you for the video, very helpful!
Alternatively you can think any point on the plane satisfies ax + by + cz = 10 so you can replace the second grouping corresponding to the point on the plane with 10 so you don’t get confused by the sign of d.
Hey Dude, your explanation is amazing. I want to ask, how to find the closest point from a point to a plane or line. If you've explained it in another video, please let me know. thank you
I don't think he's gonna let you know
well explained, thank you!
When u doing a face reveal
sus
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AMONGUS
Even God can't explain like you!
Thank you so much man
I love you. So much. You have made math so powerful and fun in my puny little brain. You better be making millions of dollars from this.
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cool derivation thx
My hero!
might actually pass my linear algebra midterm now
phenomenal
makes sense! Thanks!
Good one bro
00:02:25 where he says "D is the absolute value of the scalar projection..." he writes "D = comp n B" on the blackboard. I'm not sure what that means exactly or did I misread what he wrote. Anyone have any idea?
So, if you dot B and n, you'll get the projection of B onto n (which is basically what dot product is). But, if you see carefully, the projection B makes on n is equal to the distance D. That's why he wrote D = comp of B on n
comp = component?
@@karanveercheema2975 Yup
Very helpful Sir thanks alot..........btw, what if there are two plane equations, how do you go about solving them?
Why are we considering the plane 6x- 3y+2z= 10 to be equal to n vector instead of the horizontal plane perpendicular to point p as depicted in the video?
same questionnnn :( ?
excelent vid!
Thank you sir
Please do more videos on AC electricity
Can you please do a video on Commercial Arithmetics (Tax)?
I have a lot of questions.. why is n a,b,c isn’t n a normal vector and a,b,c is the equation of the plane ?
Why not just find the line equation (we have direction and position vectors already)? We then substitute x, y and z of the line into the plane equation and solve for the paramater. We then obtain the parameter that we can use to calcualate the point that lies on both plane and the line (which means exactly under the point we are looking for). Then simply calculate the distance between two points and we have the solution.
thankyou so much
verygood thanks bro
Thank you
Please teach vector analysis
Damn these videos from "2006" are helping
Does anyone know if he does statistics videos? He helped me get an A in algebra1 and an A in algebra2. Now onto stats next semester which I haven't a clue what I will be learning 🤯
he does! Search it up please
Are you sure D should be -10 and not +10?
I love u man):
thanks !
How do I find k if the distance k,0 and 2k,0 is 10 units
Must the line the point makes with the plane be normal to the plane?
yes that's the shortest distance
I’m not in calculus but I’m watching this lol
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if it is as you just said, the magnitude of n should be equal to the distance b/n the point and the plane, i don't get the logic
I don't understand why vectors a and b were then compared to vectors n and B, if n is taller then a?
What about the shortest distance from a line to a point?
Thx guy
Why is vector n = (a,b,c) parameters of the equation of the plane? How do you know it?
Please explain how we got d, i got everything else
Thank you
the goat
I wish I had just followed your videos and not spent weeks trying to decipher our damn textbook, written by a mathematician, for mathematicians... not for students.
Thank
What happens if the point is not perpendicular to the plane ? Would you still be able to use the scalar projection of b onto n to find D (the distance)?? Anybody know ???
thx
Hi can u help me with my algebra 2 homework reply if u can ! (;
sorry, why was the denominator the square root of a^2 +b^2 + c^2 please? why is this put in the formula for D, or just from a standard formula?
The distance of a point n with coordinates (a, b, c) from origin is denoted by |n| and is equal to sqrt(a^2 + b^2 + c^2). This is from the equation of distance between two points and substitute the second point as origin i.e (0, 0, 0)
Oh, okay thank you so much, so he substituted the n in, so we have to generally know this square root part or do you know how it was derived, i don't want to confuse but would it be from the a^2+b^2=c^2 formula? Thanks
i love you
thx ^^
very goood
actually there is(in my opinion) a simpler way to do it
what is the simpler way?
Thankssss
I need to find the distance between two planes
find each ones position vector, and then use the distance formula
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why not just find a piont on the plane and do it from there, it's much simpler
i love u
well
Oh yeah
Got first comment.
支
I want to see your face.
thats kinda sus
:-)))))
First
thx so much
Thx