Volume of the parallelepiped determined by vectors (KristaKingMath)

Learn how to find the volume of the parallelepiped given three vectors.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[BCTheKilljy]

For anyone who is curious; you can also do abs(b.(a x c)) or abs(c.(a x b)) or abs(a.(c x b)). If you analyze the parallelepiped figure, it's essential the same thing, being base times height. Just a lil' tip. ^^

[-a]

You are an absolute queen, my professor couldn’t explain it but you could!

[Chris-nqri]

Followed your vids for 10 years and you made me love Calculus/Linear Alg/Geometry/etc even today. Working on Linear Alg Final. Thx!! Ftw!

[AlanAC]

Wow i love your voice. I'm actually watching this again like an ASMR.

[deanastasia]

I just found this video today. Extremely helpful! thank you!!

[sophievthomson]

thanks for video i understand it all right up to the last point-in order to find the magnitude of a.(bxC) why do we not take the square root of 2^2+16^2+9^2?

[rejoicedube]

Thank you! i will definitely watch your calculus 3 vids to get the jump on next semester

[hotinhung]

Just left my notebook in school the day before exam. Extremely helpful!!!

[Goggisploggis]

Hi! Isn't it possible to just find the determinant of the 3 vectors instad?

det([1 2 3; -1 1 2; 2 1 4])

[cirkmannzirkel]

Could you also show us how to do it with triple integration with given points? Thanks

[exoticcoder]

This tutorial is super clear ! Thank you !

[lrdrskillz]

how does the cross product of two vectors give you area? Doesn't it give you the vector orthogonal to both? How is that area?

[rosiesennett]

omg thank you for just... explaining it. I so appreciate you taking the time and sharing.

[rishabhsingh]

this video was very helpful, I was actually searching for video which would prove how triple product denotes volume and this one was perfect thank u

[whomisac]

Hi. How do you proof that they are in the same plane? I have got a question like that in my quiz but I don't know how to?

[sifatraihan]

Your voice is so lovely and thanks for teaching this.

[gmjmoviereviews]

Watching this in 2022...So so satisfying!

[SandraGonzalez-ovtt]

I love your videos! They are so helpful, thank you!

[pablobiedma]

We can also do the determinant of the three vectors right?

[kgotsoshadrack]

hey krista king you made it clear thanks sister