Dot and cross product comparison/intuition | Vectors and spaces | Linear Algebra | Khan Academy

Dot and Cross Product Comparison/Intuition

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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

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[MrYw]

I'm studying engineering at a "world class" university and you explained better in this ~20 min video than any of my prof did in a week

[chitraraj]

THANK YOU!!! This was priceless to me. You explained in 10 mins what my professor couldn't in weeks. It's amazing how easy you make it all seem. Thank you sir! College professors should be required to watch your videos before they attempt to teach others!

[stjoeshs]

I very much appreciate the service you provide here. Too often I've had to settle for simply memorizing a formula or process just to get through questions. You provide clear explanations for the concepts presented by these topics, and that to me is a most valuable thing. You outclass a great many professors in your teaching style.

[ScorpiaX]

Thank you so much.
I have a better intuitive understanding of vectors now...
My calc teacher just says the cross product gives you the area of the parallelogram without explaining anything, this definitely clarifies it for me.

[janakruia]

This man is responsible for restoring my interest in physics (after it has been sucked out by the "professors" that teach me in the institute), by explaining the logic behind how the things are working!!

[zhannqiya]

thanks Sal, I've been confused with the differences of these two things for weeks and your video is the exact answer i need. thanks a lot❤

[AlexeyYunoshev]

Thank you so so much! It is so satisfying to understand the intuition behind it. Such a great explanation.

[khyatikejriwal]

This video is all a student driven by the question why you!!!!

[tszho]

THANKYOU VERY MUCH!!
What I want is "understanding" the meaning....
This vid helps alot!

[atmjahidhasan]

Watching the full playlist in just one night. -_-
Learning Linear Algebra in a whole fu*king night! -_-

[heavydutyloader]

Finally it becomes clear to me. Why explain in such a difficult way, that most teachers do, when you could explain it as easy as it is. Like this?

[User-cclz]

you are the best one to make intuition of things

[WonderlandOverture]

Thank you SO much! This is exactly what I was looking for--your explanation makes so much sense.

[vigneshbk]

Thanks a lot.. !! I will mark my words here.. if become better in my life I will surely find this channel..!! 😍

[chewch]

Great explanation! This video is so much understandable than any kind of "reference book". Really appreciate this one.

[armageddon.]

Finally a video that compares both dot product and cross product, really helpful, thanks a lot :D

[MisterTutor]

Speaking of going off on a tangent, the tangent of the angle between the vectors is the ratio of the length of the cross product and the dot product :)

[dianaduque]

this is exactly what i have been looking for, its the perfect way to join the concepts in your brain to something graphic you can analize. Gracias desde méxico!

[aeroscience]

That was the best. It makes much more sense when you get into the intuition. Great video, subd.

[dariopy]

@comecra85 It's just defined that way. The concept of cross product was basically "invented" as a vector.