❖ Volume of a Parallelepiped Using Vectors (Multivariable Calculus) ❖

In this video, we uncover how to find the volume of a three-dimensional object determined by vectors using magnitude, dot product, and cross product! 🌌📏

Join me as I demonstrate the process to calculate the volume of a parallelepiped formed by three vectors. We’ll also explore how to determine if three vectors are parallel—if the volume is zero, then the vectors lie in the same plane!

What You'll Learn:

How to compute the volume of a parallelepiped using vectors
The significance of magnitude, dot product, and cross product
A step-by-step guide to show if vectors are parallel
Visualizing the relationships between vectors in 3D space
Whether you’re a student tackling vector calculus or simply curious about 3D geometry, this tutorial is for you! Don’t forget to like, subscribe, and hit the notification bell for more engaging math content!

Keywords: volume, 3D object, vectors, magnitude, dot product, cross product, parallelepiped, vector calculus, math tutorial, geometry, STEM education

📚 For more resources, check out the links below!
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💬 Questions or comments? Let me know below!

#MathTutorial #3DGeometry #Vectors #VectorCalculus #Volume #Parallelepiped #STEM #LearningMath

[webgpu]

this video has a duration of "PI" minutes :-)

[patrickjmt]

i have faith that most people can do keyword searches with a large amount of success

[aimanjamil]

thanks. every year new students will come and search for something like this.

[engeeringtopics]

Thank you so much for taking the time to make such great content.

[AznPryde]

I really enjoy your videos of math examples. I haven't seen all of your videos, but have you considered doing physics problems too? Cheers!

[ken]

In my textbook, you can just find the determinant of the 3 given vectors. the volume is the absolute value of the det. 

[huzaifasaleem]

Your video helps me a lot . Thank you so much

[dancinmad]

You are misspelling parallelEpiped. I'm not trying to be an ass - just thought you might want to know. Btw, thanks, you're videos are being a great help for some last-minute review before my Calc 2 final. 

[gateclub]

Beautiful but we can directly use scalar triple product to find the volume

[williamnguyen]

You're a champion! Keep doing what you do!

[nostrasummit]

this was wonderful! I understood it first time I watched it

[evilHVgenius]

umm when taking the cross of two vectors I'm pretty sure the sign before the j or y is positive, it is different then just taking the determinate. If you put the minus there you can end up with a volume of zero because it subtracts any volume in a negative region.

[yEllis]

This was really helpful .very easily broken down .. 

[patrickjmt]

i understand, but maintaining playlists with 1500 hundred videos is a bit of an organizational nightmare.

[shrashtimandloi]

Thank you very much bro ✊. It is very helpful to me.

[Nickuncle]

They're very tightly related. Many Mathematics and Actuarial majors at my school take both together.

[harvins]

If V=|(a•b)×c|, there is no way to find the magnitude right?

[audreymartin]

how do you know, with just the vectors, which vectors should be crossed and which one should be dotted?

[AKTxITACHI]

how would this world if they gave me 3 vectors with 4 rows? do I just ignore the 4th row?

[marctrran]

Hey Patrick, could you please do a video where you work out the equation of a plane just given two lines that are parallel?