Finding area using cross products | MIT 18.02SC Multivariable Calculus, Fall 2010
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- เผยแพร่เมื่อ 1 ก.ค. 2024
- Finding area using cross products
Instructor: David Jordan
View the complete course: ocw.mit.edu/18-02SCF10
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
I like how clean the chalk board is. It's a sign that you took care of the small things/presented well.
It's MIT. They actually take the time to clean up before and after each lesson. :)
Hi how old are you
That helped me so much thank you I might just have gotten a much better mark in my test because of this video
Fantastic explanation. Thank you.
Well explained. Love it. Please do more videos on the topics of calculus 3
Thank you !! It was very important for me
Nice explanation! Thank you.
Thank you, this video is very helpful.
tnx! you really helped me out! :)
Understood the topic.Thanks sir
he made a mistake...when computing the cross product he wrote P1P2xP2P3, he was supposed to write P1P2xP1P3. All of his work is still right but that was just a simple mistake.
yeah
me too .thanks
This is not a mistake. It's a triangle. From the picture it could be seen that you can choose multiple combinations of vectors. As you pointed, you will get the same answer. Please check your facts before pointing mistake on MITs side :) Usually, it's just not so.
@@HoudekM You replied to an old comment for one, but for two -- go to 2:55. OP is correct in saying that the presenter wrote the incorrect cross product on accident, but did the correct work. Rather than "P1P2xP1P3" he wrote "P1P2xP2P3", but again, did the correct work for P1P2xP1P3. Please check your facts before pointing out a mistake on Sergio's side :) Usually, it's just not so.
If you're trying to find the area, it is the same. You can take opposite vectors and it will be still the same result. If you draw the picture, you can see it.
On almost every other OCW video there is some comment about MITs "mistakes". That's why I commented on this one.
@@HoudekM Yes, I get you. But the only mistake noted here was just a simple inconsistency in labeling, not math. That's it. No biggie at all :P
OP didn't mean "It has to be labeled correctly or it doesn't work!". He was just saying, "Hey, there's an inconsistency in labeling, but it's all correct nonetheless -- just a simple mistake." You get me?
Great video!!!!! Thank you
Just explain where did you get that 3 sqrt(2) from at 4:12 !!!
modulus of is ((3)^2 + (0)^2 + (-3)^2)) = 18, Then sqrt(18) = 3sqrt(2)
It’s just the magnitude of the vector that he found he just did it in his head real fast
:(
Kevin Lewis that’s not hard to do in your head. Especially if you work with magnitudes often...
You need the magnitude of the parallelogram in order to know its area. A vector cannot be an area. So he took the magnitude of 3i-3k
Thanks from Algiers.
This was useful , thanks :)
thank you so much sir
Is it similar to Area = base×height? Also, what if you are given scalar quantities in cm? Also, doesn't cross-product get you the normal?
Thanks 👍
Very good job
Thank you!!!!
Bhaiya u taught so well thanks
Thank you
@ducati23march any two sides because you will always get the cross product thats perpendicular to the triangle
Nice explanation
It helps in my jee exam
I love how he skipped over squaring the XYZ components, adding them and taking the square root; that messed me up until I thought about magnitude as length
bro im still fking confusd
@@daveedharb9925root 18/2
THANKS
Thank yooooooou!
nice and clear explanation, thanks
ty very much
my question is why we take cross product why not dot product while finding area of triangle ???
thanks a lot..
thanks sir
thank u
hey...u solved my problem
4:18 How do you get 3*sqrt(2) from [3 9 -3]? :S
Shouldn't it be sqrt(3² + 3²) = sqrt(18)?
sqrt(18) = sqrt(2*9) = 3 * sqrt(2)
He probably had used simple trigonometry .
Is it OK if we take p1p2 x p2p3. ??? Plz answer
Good video, but when referring to magnitudes or lengths of vectors, you should not say absolute value (this is used for numbers). You should say magnitude, modulus or length to distinguish from scalar quantities.
Norm
Using the absolute value brackets is standard notation for the magnitude of a vector value.
Watching in 2020 from India
This vid is for which course of students?
Tq u dear
There is a mistake there, it should be p1p3i instead of p2p3 on the last part i think
Thank you very very much . I'm from Iraq
so we dont do a1,a2,a3 b1, b2, b3 c1,c2,3? or is this different because it is asking for the area?
c3*
I dont understand on last step plz explain sir
3,0,3
=3squareroot 2
How is this step
modulus of is ((3)^2 + (0)^2 + (-3)^2)) = 18, Then sqrt(18) = 3sqrt(2)
bruh when he said hell be back in a minute 🤣🤣🤣
how did he get 3root2 all of a sudden?
root of the sum of squares of each component so root(3^2 +0+3^2)=root 18=3root2
Omg seriously I was like what the hell did he do
He should have explained, bad educational example
@@J1hn1 it's such a common sense . Why you need explaination for such a simple thing ? And he did say "we need the magnitude of this vector" . That obvious clue wasn't enough ?
@@darkseid856 No.
The sheer fact that Indian Education taught us this when we were in 11th Grade 😂
Average toxic Indian spreading their stupid propaganda and spoiling our nation's image
why don't you choose P2P3 either ?
will it matter if I use different vector, say for example P2P3 and P3P1?
+ChileMarie Santiago
I am actually here on the same question.
My maths teacher says no, as long as they end at the same points. But I am not so sure :P
The end points or the starting points, either of the two need to be same. Like if you want to start with P2, you must have P2P3 X P2P1. Similarly if you want to end with with P2, it should be something like P1P2 X P3P2. I hope you get what I’m trying to say
how badly i like MIT,
😀
V 1 V2 P 1 P3 2X AREA OF TRIANGLE IS EQUAL 3 ROOT 2
good
How did i got here
At 2:53 it should be p1p2 x p1p3. U wrote p1p2 x p2p3.. Like the video regardless
THE AREA OF THE TRIANGLE CAN BE FOUND
If we erase his knowledge of determinant and all his memorised formulas, will he be able to derive an area of parallelogram, given 2 vectors?
In other words, does it make sense for him when he multiplies numbers and subtracts number what he actually does or he just follows blindly what he has read before?
What if the determinant of a matrix doesn't produce an area of parallelogram?
An Indian student must be laughing after reading the comments, isn't it?😂
i did not get most of this....
It's worth it to try. First of all, this is geometrical. Geometry is the universe. Linear algebra is about systems of equations and polynomials which really has little to do with geometry but there are some connections you could make. This requires no knowledge of systems of equations and polynomials. Think about 3d game programming. If you understood this and dot product you would get pretty far. The two are very simple if you think about.
Try the 2d version of torque. r⋅(sin(theta)⋅force). Make it into a triangle. Not the right triangle, the other other one . A right triangle is too easy. r is one side, force is another, and make it an obtuse angle. Break it into two right angle triangles, or find it with cosine law. It's a parallelogram, not a triangle. You'll have to double the area of that triangle to get the area of the parallelogram.
Any time you have three vectors there will be a plane that connects them. In that plane you can make a parallelogram. It's just the way the real numbers are in 3d.
Oh, and I have grade 12, so don't take my word as the holly gospel.
P1 P2 P3
P2 - P1 121
P1 P3 - 1 AND WE GET 1
0-1 = +1? why?
+Brunin G3 neri You are missing a minus sign, the calculation is: 0 - ( -1) = + 1
Great video :D
The chalk board looks like dark chocolate bar
oh so these are points not vectors thats y u did it this way i see
Points are vectors =)
MIT teaches such basic maths .how vulnerable
even a 17 year old student in india can solve it
Hi
An 11 year old child in China can solve it
So ? What that has anything to do with the video ?
111
🇧🇷⚙️
Is it just me, or does he kinda look and sound like Mr. Beast...
Indian tutorials are better
4:18 How do you get 3*sqrt(2) from [3 9 -3]? :S
Shouldn't it be sqrt(3² + 3²) = sqrt(18)?
it was the absolute of the cross product buddy