Volume of a Parallelepiped Using The Triple Scalar Product Calculus 3
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- Опубликовано: 15 окт 2024
- This calculus 3 video tutorial explains how to calculate the volume of a parallelpiped using the triple scalar product formula.
3D Coordinate System: • Plotting Points In a T...
3D Distance Formula:
• How To Find The Distan...
Equation of a 3D Sphere:
• How To Find The Equati...
Calculus 3 - Intro to Vectors:
• Calculus 3 - Intro To ...
Calculus 3 - The Dot Product:
• Calculus 3 - The Dot P...
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Angle Between Two Vectors:
• Finding The Angle Betw...
Parallel & Orthogonal Vectors:
• Are The Two Vectors Pa...
Direction Cosines and Vectors:
• Calculus 3 - Direction...
Calculus 3 - Vector Projections:
• Calculus 3 - Vector Pr...
Cross Product of 2 Vectors:
• Cross Product of Two V...
_______________________________
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...
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Hey The Organic Chemistry Tutor! In the future can you do more Calc 3 videos? Like about equations of lines and planes, quadric surfaces and cylinders, thank you so much you are awesome.
Watched this for fun and ended up getting a parallelepiped volume problem in my recent exam! Lifesaver
For fun is crazy, good for u though
Professor Organic Chemistry Tutor, thank you for explaining How to find the Volume of a Parallelepiped Using the Tripled Scalar Product in Calculus Three. I also encountered this topic in Engineering Statics and Dynamics. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
The Organic chemistry tutor, you are literally going to make me pass my university entrance exam. Thank you
Good bless, I need more on Cal 3 my test is in 2 weeks, proffessor making insine problems, I dont know if he think we all want to work for NASA or something like that...
Had to check for myself if it actually was equal to the determinant. Am truly mind blown🤯. Thanks for the easier method 🙌
thanks man. your vid helped me even after 5 years!
Since the scalar triple product isn’t commutative, how do you make sure that you are doing the cross and dot product of the vectors in the right order?
yes i also want to know ,,cause when i tried it i did it in the wrong order and got -54 instead
Amazing explanations and drawings! I like the comparison of the formula to that of finding a regular volume. That made it super easy to understand!
How do we know that the área of the base is the cross product of v and w, doesn't the cross product of v and give you the vector along the z axis?
One thing to note: It doesn't matter wheter you put the vectors in the rows or in the columns of the matrix, because the det A = det A^T (where ^T = Transpose of). I think this is easier to remember. Just put the vectors next to each other in a matrix, and then calculate the determinant of that matrix.
For example 2, how do you know which points to pick (apart from the origin) to find the vectors?
You can honestly use any points it doesn’t have to be that 0,0,0 point know As the origin . It can be any other point but that has to be the point where the other vectors start from if that makes any sense
Hello, How do I know the area is bounded by v and w but not v and u or w and u? The height must be u? why choosing u as the height?
What if we exchange v*w by w*v why you chose that
this is just what I needed for Calc 314
what happen when u get negative ? just negate the symbol ?
i tried it but got negative, but the answer is right without them
that's cause the original formula is actually the absolute value of the triple scalar product, it's something I noticed that he didn't mention in the video so good to know as a heads up 👍
The product can be positive or negative, it determines position on a plane.
His the best we ever had ❤
For Which standard this topic is?
2:06 it doesn’t makes sense to me because you just said A=||VxW|| but in the equation it is written as (VxW). You have to clarify.
Yeah he gets mixed up a little. v x w gives a new vector orthoganal but with length equal to the area. This becomes super useful because u . (vXw) is the projection of u onto that orthoganal vector times that orthogonal vectors length (which is the area remember) - and the projection length is the Height.... so it all works out beautifully - that dot product gives us the H times the Area which is the volume of a Parallelepiped
What I don't understand is why not just calculate the determiniant of the 3x3 matrix using the three vectors - that gives you the volume of the transformed 1x1x1 base vector cube which is the volume of the transformed cube = Volume of the vectors parallelpiped
One question tho
I thought determinant only worked for cross products how come we're including the first vector which was supposed to be dotted, to the matrix
I know right? Perhaps Mr. Chem is wrong. However, I solved the problem in a trifle bit different way; first I calculated the area of the Parallelogram ABCD, then I quantified vector AE. Finally, I multiplied vector AE with |V×W|. However, bamboozledly he achieved the same answer as I got!
Please explain the modulus of a cross product of two vectors represents area between those vectors?
One question, what is they give values of all four vertices
you are god of teacher
Uffffffff! How Amazing of You....Thank You Sir
Does the order matter in the triple scalar product?
No
@@theadel8591 Answered your own question?
@@alienwarex51i3 yup I answered my question after I looked it up so that if someone has the same question could find the answer.
@@theadel8591 Bless your sould
Thanks I was actually looking for the answer to this exact question!
how is this calc 3 if im learning this in precalc?
this guy is the greatest
Xan someone please explain to me why it is MINUS 3 instead of plus 3?
where exactly lol?
that's how a 3x3 matrix cross product works. the middle 2x2 matrix is negative, and the first and third 2x2 matrices are positive. 4:30
Wikipedia: Cross_product#Matrix_notation
expain further plsss@@jinnjinn5567
What is the new volume of parallelopiped if I turn any one vector 60 degree anticlockwise..
did you complete calc 3 playlist? :0
God Bless U brother
how come you chose vectores AB and AD? without drawing the object, which in some cases i can not cause idk how to visualize co-orinates, how do i know which 3 vectors i need to use? i tried using the dot product of any 2 vectors should be 0, but i quickly found out that since AB has 2 zeros in it, and its the only vector with 0's in it, no other vector could have a dot procut of 0 with the vector AB. so if i cant use dot products to see which vector i need to use... which vectors do i use? cause apart from the drawing, u seemed to randomly pick ones that work
i tried randomly picking AC, AE and AH, and i got a tripple scalar of 110 which is obviously wrong.
there is no line AC or AH
But how do you know without drawing it
i suppose he created the problem based off his own drawing. i'd assume exams would also have a drawing in the case that they provide a bunch of points like that
Thanks sir
Thank you my life saver 😊
Thank you very much
my saviour
I have doubt man...Why do they call them Coterminal vectors in some questions..while they are clearly co initial vectors 🙄🙄
But WHY is the cross product of u the height..
1:10 1:37
2:05 2:48 dd
2nd Problem 6:58 9:00
Very helpful
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Thank you so much :) !!!
What if the answer is negative
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I can't see the question
Life saver💖 UwU 💖
how to find the volume of a parallel lalala pipi
Thank you sir.