Dot and Cross Product Comparison/Intuition

[MatthewHan95]

which subheading are vector videos in ?

[icoscx]

TY!!!!!!!!! I finally passed my Linear Algebra Exam!

[Guille3692]

OMG! Soh Cah Toa! Of course! That's genius, really, if only i knew it last year....

[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.

[omgthatscrazyx]

you're doing such a great service to the world. THANKS!

[SB9101]

Why do I go to school? I learn more this way!

[s2000gpw]

Just ridiculous how much this video helped. Could not have been anymore informative and intuitive. I have been watching your videos for a year and a half now Sal, and I can honestly say they have changed my life. I have gone from a kid who failed math in high school to a math major at a major university. People would have to be out of their mind not to watch your videos and get what I have out of them. Your teaching methods had better b the foundations of our education system in years to come.

[stevenydc]

what program are you using in the video?

[bugfacedog44]

"This was a bit of a tangent"

I laughed

[TerryCrimson]

Good video! And the subtitles make it even better! Thank you very much!

[netroware]

"This was a bit of a tangent" -- Oh dear. :-D

Sal, you're brilliant.

[pussiestroker]

Very intuitive!

[diegosjimenez]

I learned alot from this video. thanks, this will help me on my midterm.

[chitraraj1]

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!

[myonlynick]

If you don't want all the theory bla bla,skip to the GIST: 12:01 - 13:05 (a.k.a intuition)

[LAnonHubbard]

This is all very interesting.

[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?



[nrod2712]

This video gave me goosebumps, it was that good!

[comecra85]

The one thing I don't understand in your video about cross product is why is it vector. Why the crossproduct is not defined as scalar like dot product but with sin (0). That is axb = |a|*|b|*sin (angle).

Why dot product is scalar and crossproduct is not?

[dariopy]

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

[Halo276]

Just a question, so we can find the area of the parallelogram as simply just "a" vector cross the "b" vector. Does that mean the area of the parallelogram is also "b" vector cross "a" vector?

btw, thank you for all your videos they help ALOT =D

[Taowhr]

@Halo276, order matters in the cross product, so a x b does not equal to b x a

a x b is equal to -b x a however. That is an identity

[dalcde]

" Just a question, so we can find the area of the parallelogram as simply just "a" vector cross the "b" vector. Does that mean the area of the parallelogram is also "b" vector cross "a" vector?"

The length of the resulting vector is the same, but the cross product is a vector! The normal vector would be the opposite direction if you use b x a instead of a x b according to the right hand rule. Taowhr said that a x b = -b x a, which is true, as the direction of the normal vector is inverted.

[Rickroll604]

can't like this enough

[riskylulz]

You explain things amazingly. Thank you!

[WonderlandOverture]

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

[AtlantiXYL]

yout tablet is much better quaility now.

[jubeidono]

Thanks sal! Amazing videos keep up the good work.

[UndeadTheta]

Great video!

I do have one question (perhaps I misunderstood) about the parallelogram at the end. I believe your equation would only work if the parallelogram was composed of 2 right triangles. For parallelograms composed from general triangles, I got:

Area = base x height

= ||b|| sqrt( ||a||^2 sin^2 (theta) + ( ||b|| - ||a||cos(theta) )^2 )

[alkalait]

you are wrong. height is also the opposite of theta. so sin(theta) ||a|| = height. just remember soh cah toa.

[ImTestingSleeping]

Thank you!