Volume of a Parallelepiped Using The Triple Scalar Product Calculus 3

This calculus 3 video tutorial explains how to calculate the volume of a parallelpiped using the triple scalar product formula.

3D Distance Formula:

Equation of a 3D Sphere:

Calculus 3 - Intro to Vectors:

Calculus 3 - The Dot Product:

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Angle Between Two Vectors:

Parallel & Orthogonal Vectors:

Direction Cosines and Vectors:

Calculus 3 - Vector Projections:

Cross Product of 2 Vectors:

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Area - Vector Cross Product:

Triple Scalar Product:

Vector Equations of Lines:

The Equation of a Plane:

Planar Equation - 3 Points:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[Deoxys_da]

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[holoboy]

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[khoanguyen]

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[zackfoster]

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[alexanderquilty]

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.

[KaelHitchcock]

Watched this for fun and ended up getting a parallelepiped volume problem in my recent exam! Lifesaver

[salomemartinez]

The Organic chemistry tutor, you are literally going to make me pass my university entrance exam. Thank you

[georgesadler]

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 YouTube TV with the Organic Chemistry Tutor.

[christopherpowell]

Had to check for myself if it actually was equal to the determinant. Am truly mind blown🤯. Thanks for the easier method 🙌

[caesaryumury]

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...

[nutella]

thanks man. your vid helped me even after 5 years!

[timokuiz]

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.

[memeingthroughenglish]

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!

[fordemacia]

For example 2, how do you know which points to pick (apart from the origin) to find the vectors?

[blakeelzinga]

this is just what I needed for Calc 314

[ravemaster]

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?

[PGTips-slmq]

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?

[YonatanAndualem-bl]

What if we exchange v*w by w*v why you chose that

[Cleoclementi]

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?

[rajajaladurgam]

Please explain the modulus of a cross product of two vectors represents area between those vectors?