Dot and Cross Products (Real Physics)

[@6tanglewood]

Two comments... 1) You use the term perpendicular when you really should be using orthogonal. 2) When calculating the determinant of the 3x3 for the cross product, shouldn't you be SUBTRACTING the product involving the j-hat unit vector?

[@jg394]

1) Yes, orthogonal is probably more precise. This video is aimed at people who have worked their way up to calculus, so they are probably not familiar yet with the concept of orthogonality in linear algebra and such. (The concept of mathematical spaces and such is way beyond the intended audience's ability.) 2) Remember that if you reverse the columns (or rows) the sign of the determinant flips. Note carefully the order and you'll see my notation, though not really standard, is correct. It's how I've remembered it.

[@XanderGouws]

Is this gnna develop into a series on vector calculus (and/or multivariable)?

[@jg394]

It was originally a video I did for my Introduction to Electrodynamics series. It blew up for whatever reason so I'm redoing it. It looks like it's going to blow up again. But to answer your question, yes I do plan on doing at least the fundamentals of multivariable calculus. I have a book I love called "Mathematical Methods in the Physical Sciences" by Mary Boas that I will do before I tackle Quantum Mechanics. You really can't do quantum at all until you get some math chops first.

[@XanderGouws]

@@jg394 I'm looking forward to it :) Is it similar to _Mathematical Methods for Physics and Engineering_ by Riley, Hobson, and Bence?

[@jg394]

@@XanderGouws The one I have is by Boas. Does it cover imaginary numbers, multivariable calculus, probability, infinite series and other topics? If so, it's probably similar. Basically, everything math students learn in undergrad condensed down into a 1 year course for physics students. (Who needs proofs anyway?!) Join me on Discord: discord.gg/TGK47Pf

[@manojbhardwaj5400]

What are you starting ?

[@jg394]

This was a re-do of a video I did a long time ago that has been consistently my #1 video. I worked up enough courage to redo it.

[@jbroooks]

Does this work with a different coordinate system? like cylindrical?

[@jg394]

You'd have to convert to cartesian coordinates first.

[@amogh5427]

11.30 pm... Sleeping... Beep Beep... And I am here

[@anujgupta3381]

Tysm ❤

[@davidmurphy563]

Nobody ever explains how the determinate is meaningful..

[@jg394]

It has a geometric interpretation but in my mind it simply represents how "big" the matrix is. You end up dividing by it to scale things.

[@padmasrirampalli9687]

(a.b)square+(a(cross)b) square=144. If a=4,then find b

[@padmasrirampalli9687]

Please answer this question

[@cristinafelix5468]

It really bothers me the sound of a sharpie on paper. Regardless, thank you for the videos.

[@ruzzcraze1862]

Asmr