Area of a Parallelogram Using Two Vectors & The Cross Product

This calculus 3 video tutorial explains how to find the area of a parallelogram using two vectors and the cross product method given the four corner points of the parallelogram.

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:

Vectors - Free Formula Sheet:

[faichalayeva]

Tell us about yourself, what did you study in college, etc.. Please answer.

Thanks for the uploads.

[EM-duch]

you broke it down really well thank you so much! I love how you give the basic idea first and then you give a more detailed example really helps in knowing what you are doing when you apply these things

[georgesadler]

Professor Organic Chemistry Tutor, this is another classic video/lecture on Finding the Area of a Parallelogram Using Two Vectors and the Cross Product in Calculus Three. This is a classical problem in Advanced Mathematics. This is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.

[phikopk]

This guy is the best
im from South Africa

[romanaiqbal]

thank you for this detailed explanation! Extremely helpful

[Reem-opws]

Would you talk about how u keep all the information u know about all subjects so u don't forget them?

[joyyang]

how do u figure out which two sides to pick (2 adjacent sides)?

[moeisthis]

Why do you minus the middle unit vector j and get positive values for i and k?

[chenyushang]

How do you determine which value is u and which value is v???

[kimayapanash]

i made my friends jwalous with your last video too

[brittybabii]

you're amazing thank you so much!

[cristal]

was the formula 1/2 |AxB| ? is the answer suppose to be 6 unit squared? I might be wrong I might be mixing up my area of triangle vs area of parallelogram. Thank you.

[mukundnarayanjha]

Great explanation, helped a lot, , thnx mayn!!!

[DeluxeSlayer]

I already knew the formula but I came here hoping for an explanation on why the magnitude of the vector gives you the area of the parallelogram. Anyone please? Id really like to understand this concept

[ogbanyajuliet]

Thank you so much sir but do we need to add Unit?🤔

[thenetworkguru]

My guy, please touch on perimeter of parms and orthogonal projection and complement please @organic chemistry tutor

[arishbamemon]

Why do we calculate the magnitude of cross-product? What's the purpose?

[Meemeedeeyap]

It would be great if you separate your calculus lessons playlist, it’s confusing when you don’t know where cal 1 ends and cal two begins

[MrSidTaylor]

The statement that the area is given by 1/2 mod(AXB) is an assertion which has not been proved.

[LolaGunter]

is Area = | vxu | for every shape or just parallelograms?