Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! In this video, I give the formula for the cross product of two vectors, discuss geometrically what the cross product is, and do an example of finding the cross product.
For more free math videos, visit http://PatrickJMT.com

Text Comments (563)
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Ryan Dunne (19 days ago)

I am watching this as a quick review for a class, but thanks you're videos got me through calc 1-3 and ODE. You are the reason I am gonna graduate with my engineering degree, thanks!

patrickJMT (18 days ago)

time to be a patron on patreon! :)

saad mohammed (22 days ago)

perfect!!! thanks

Zeina Ghanem (27 days ago)

I was absent from school for a whole week because I got very sick and this lesson was taught in my absence, thanks for this video I know now how to solve what he explained

habtamu worke (1 month ago)

You, my good sir, are an example of a good person. what is the difference between cross product and matrix multiplication?

Tarik Hacialiogullari (1 month ago)

HEROOOO THANKSS!!!! <3

Ice Queen (2 months ago)

Thank you! Yay! I understand now! I hate Early Transcendentials. They are so abstract, it's hard to understand.

Andrew Seelig (3 months ago)

sounds like leafy

Бекнур Даулет (3 months ago)

hello SDU

anupama cm (6 months ago)

what happens when the subtracted value is negative in j. does it changes to positive component?

kent Chavez (6 months ago)

Thanks man I appreciate.

Kanivakil (6 months ago)

Wish you weren't a left handed; have to wait for your hand to lift up if I didn't pay attention to what you said. However, it is proven that both right handed and left handed people both could do math.

Jerry Addison (6 months ago)

How about 2D vectors? Im assuming I replace a3 and b3 with 0?

WAYCEE HARVEY (6 months ago)

I'm taking Calculus Based Physics 1 this semester and we're reviewing vectors. However, vector cross products seem a bit different in physics or maybe it's just me. But I been stuck on a question for several hours now and need help!

Abubakr Ismail (6 months ago)

God sent

Adventure of CR (6 months ago)

patrick !! how the sign of -- come before j ??

George Shum (6 months ago)

my mans patrick sounding depressed as hell in this vid

Palasamudram Sreevani (7 months ago)

anyone noticed that he is a leftie?

Emily Schwartz (8 months ago)

You saved me from failing

dinesh chauhan (11 months ago)

Why i MINUS j and then PLUS k....why arent all subtracted or all added?

jamal khan (11 months ago)

Patrick , thanks alot you are saving my life

patrickJMT (11 months ago)

my pleasure :)
come back any time!

jamal khan (11 months ago)

This is my favorite channel during mid and final EXAMS !!

Matheus Silva (1 year ago)

You are such a super teacher!

Killian Defaoite (1 year ago)

Finally a good explanation of this! My calculus textbook did a poor job of explaining this. Really helps for calculating torque with radios and force in component form as torque = r *x* F

tan4tanny (1 year ago)

Brilliant

Xanda Jaza (1 year ago)

Thanks

samar Liet (1 year ago)

u r the best

Irfan Iskandar (1 year ago)

you have no idea how much grief you've saved me from. Thank you sooo much

cesarrulez2 (1 year ago)

Wow thank you so much Patrick, this helped me a lot in my physics class

stoneridge zutt (1 year ago)

no sound on google chrome on windows 10

Aarzoo Jaiswar (1 year ago)

Thank you so much

Aarzoo Jaiswar (1 year ago)

Thanks Patrick sir, Now I understood

Boon Koh (1 year ago)

Great video with clear explanation! Thanks, Patrick.

Elijah Achiek Panchol (1 year ago)

the video is really helpful to me, try to be little bit slower in talking.
thanks

Princess Rapunzel (1 year ago)

Hey Patric,when the j is gonna be + or -?

prince of hearts (1 year ago)

You are brilliant.

Çağrı Zorlukasap (1 year ago)

for the 3*3 determinants we have close 1 st column 1st row and for second column (j) 2nd row second column am ı rememberıng wrong?

The Duke (1 year ago)

This is my fourth math class that I am passing because of your videos. Thank you for your service Patrick

Toka Zhu (1 year ago)

very clear lesson, thanks! where you from, i love your accent!

patrickJMT (1 year ago)

grew up in the south, live in the southwest now

claireabella (1 year ago)

Is it always i - j + k?

webstime1 (1 year ago)

Yes, you can use the right hand rule to prove it.

Carly Nield (1 year ago)

Patrick, bless your soul. This is the third year of Calculus that I've gotten through thanks to your videos. You're changing the world, man.

Cristian (1 year ago)

The Calculus Gods have blessed you with a true gift!

Pratistha Singh (1 year ago)

very nice

ProLagGamer (1 year ago)

Shikamaru is that you?

Shreyas Kuge (1 year ago)

What does vector mean?

Malavika Unnikrishnan (1 year ago)

Thank you, that helped

Euric Cality (1 year ago)

thanks man!

Gabriele S (1 year ago)

Thank you - great explanation, very clear.

Sayak Maity (1 year ago)

awww...

liaqat ali (1 year ago)

why j is _ and k is +

Sai Rachakonda (1 year ago)

THANK YOU SO MUCH! I knew what a cross product is and all applications but I could never remember the formula. This 3x3 partial determinant trick is SO useful!

祁沫含 (1 year ago)

Wrong formula!!! Cross product formula should be i+j+k!

Mohammed Arsh Khan (1 year ago)

any ways nice video and helpful too

Mohammed Arsh Khan (1 year ago)

bro 1 times -1 will give us -1 not 1

Em Chotitamnavee (1 year ago)

There's a minus sign in front

Alessandro Mele (1 year ago)

Very helpful video Patrick, thanks :D

Akam T (1 year ago)

I like your videos, thank you.

Courtney Pombo De Erezcano (1 year ago)

Thank you!!! My physics professor just showed us the right hand rule, and I couldn't figure this out by that!!

Aus Taft (1 year ago)

It works!! Thank so you [email protected]#$$ much!!

oburu david (1 year ago)

You are a good physicist, i have been able to learn a lot from this video. Thank you

Pradip Kr. Das (2 years ago)

man u really did well up dude saved my day

Trevon Willis (2 years ago)

Life Saver man my Physics professor is TERRIBLE.

benjo sian (2 years ago)

i have to be a little hinest this was much more easier to understand than our computer science teacher thnx for the video rlly saved my life :D

Franklin Pac (2 years ago)

By far the best conceptual explanation of the cross product I have found. Thanks man I really appreciate it!

Curtis Haley (2 years ago)

this is why I love patrick, 30 minutes of trying to understand through wikis and math websites, he covers in the first few seconds

Jerry Smitherson (2 years ago)

Everyone's like "Dang, every time Patrick checks his numbers at the end of the video, they end up perfect".
But what we don't see is all the times he made a small mistake, which snowballed into a catastrophe that results in a deleted video and a dark night of deep reflection. hahaha

Sheraz Khan (2 years ago)

In a determinant we take that second column (j in this case ) negative but by going throught the lengthy way of finding the cross product in component form , the j unit vector turns out to be positive ..... I am getting it ... Any , explain it!!!

Garrit Clabaugh (2 years ago)

Thanks you!

gig777 (2 years ago)

With respect to the cross product.....if you have two force vectors in the same plane, how do you get a force vector at 90º to them? That doesn't make any sense. No one seems to explain this, or give any real applications. Any comments on that?

Thawsitt Naing (1 year ago)

Cross-product exists only in R^3 space. (3-dimensional)

Mehelet Abraha (1 year ago)

@GeneralSamov I don't believe u have anything different to the thousands of people he is referring to

GeneralSamov (2 years ago)

The cross product is perpendicular to the whole plane on which a and b lie. It basically goes straight out of it, like a rocket going into space from earth's surface.

Asia Akter (2 years ago)

if the cross product of two vectors is zero,what is the angle betwwen them?

Sheraz Khan (2 years ago)

Asia Akter Zero or 180 degrees if the vectors are non zero (not null) vectors , if one or both of the vectors are zero then we can have any angle from 0 to 180 degrees.

MandoEmmm (2 years ago)

If the cross product is zero then that means the two vectors are parallel, if they are in the same direction it's 0 degrees if they are in opposite directions its 180 or pi radians.

Kenneth De La Rosa (2 years ago)

thank for the prior information. Appreciated :)

James Hansen (2 years ago)

You are a hero.

Zubair Rashid (2 years ago)

thank you very much

MOHAMMED IRFAN Rajpoot (2 years ago)

Petrik
prove that
AX(BXC)=(A.C)B-(A.B)C

c.daniel Premkumar (2 years ago)

How can two vectors in a plane contribute to a vector in an orthogonal direction to the plane. It is beyond common rational thinking. Can you give a logical step by step explanation ? OR - do we have to just take it as something imaginary and say of course its true - elementary. How would you convince a student who has at least some common sense ?

Jessica Behnke (2 years ago)

Very concise, organized, and helpful. Thanks for the refresher

varun nair (2 years ago)

why did you in 5:48 take j value negative?

Thiago Ferreira (2 years ago)

because he used something called the laplace expasion to calculate the determinant. If the sum of the row and column indexes is odd then you get a minus, if it's even it's positive.

mr orange (2 years ago)

4:03 why a minus sign ? i dont get the signs

raxxor (2 years ago)

To answer my own question.. I just realized it's cause I just wrap around, works the same way but one doesn't have to remember changing the signs cause you just invert the matrice when you wrap around anyway.

raxxor (2 years ago)

Would you elaborate? So it actually means there's a plus there in some sense but it's just convention that you put a - sign before it? I've always used + signs for all of them.

quique182 (2 years ago)

thats kinda the definition when using matrices, the signs alternate. so if there was another matrix after the k it would be negative

Minh Long Hoang (2 years ago)

Thank you so much.It is really useful for me

sapcor (2 years ago)

thx alot man u helped me alote .. video published 2009 & its still saving ppl :) .. thx very much Patrick

j sjsjtt (2 years ago)

Thanks dude for the lesson

Mohith R Gowda (2 years ago)

if A B C are three different vectors and if (A X B).C=0 does it mean that all 3 vectors are in same plane

Vser Nguyen (2 years ago)

so if the problem is asking for a×b×c, if they give us points we have to find the different between them (vectors) then do the cross product of what we got. If the prob gives us vectors then we proceed to do the cross product formula as u are demonstrating here correct?

Sciencing Around (2 years ago)

hey....plz tell me what should i improve in my videos

Jesus Gil (2 years ago)

What if you're not given the components for both vectors and are asked to find the cross product of two unit vectors? Ex: j x i

MrBdc2013 (2 years ago)

yes

Rishab Maheshwari (2 years ago)

Thanks for uploading this video! Helped a lot!

Xena Chan (2 years ago)

thank you so much.I've been watching your videos since my freshman year,I'm in my second year now and you've been great help.😃👍

Prajwal Nellogi (2 years ago)

Thanks so much man but one question when do we decide to use cross product formulae or dot product formulae. Like in class I was given a question like : "Find the angle between vector a and vector b when vector a is ... and b is .....?" What do I use in this case . Could I use either one??? Pls reply. THX in advance

Kelvin Feliciano (2 years ago)

For when to use them, if they ask you find if two vectors are perpendicular. do the dot product and if the result is zero then they are perpendicular.
To find if they are parallel, do the cross product and if they result if zero then they are perpendicular.
Key words are PERPENDICULAR AND PARALLEL.

Kelvin Feliciano (2 years ago)

When looking for the angle the formula states that you will be doing dot product. not cross product.
cos(theta)= ((a dot b)/(magnitude of a times magnitude of b))

Prajwal Nellogi (2 years ago)

+ITS ME!! BTW: I'm in 9th grade

shimy (2 years ago)

does the endpoint of the two vectors needs to be the same to use cross product?

PythonDelta (2 years ago)

Needed to review this real quick for physics. When you can watch something in x2 speed and still comprehend everything, that's when u know a video's clarity is top notch.

Youssef M. Al-Aasar (3 years ago)

Thanks a lot man

SolidSnake013Duds (3 years ago)

Thank you. This video helped me out alot!

is the king? 2PAC (3 years ago)

This Guy is a genious and a great teacher perhaps!

pioneerrumi (3 years ago)

lifesaver :3

Vincent N (3 years ago)

Why is j initially negative?

Brian Wahome (1 year ago)

It is defined as a minor, You multiply it by (-1)^1+n where n is the dimension of the matrix. The first starts at 0, the second at 1, the second at 2...I might be wrong but once you're used to them you will actually never do that because the pattern is pretty straight forward. Just start at + in the first row and keep alternating with - and +, In the second row start at -, keep the process, in the third row do it like the first row, start at +, keep alternating, and so on and so forth.

Daren Brightsun (2 years ago)

+TheSummarizer That's just the derived formula for the cross product. Arriving at that -j would probably requires a different video tutorial. The important thing is that we remember it is negative.

Time Sorawit (2 years ago)

+TheSummarizer i was wondering the same thing...

aswan korula (3 years ago)

excellent tutorial, thanks for uploading.

Mohammed Alameri (3 years ago)

I am reviewing math and instead of going to read from book, I favored to watch your videos.
God Bless you man for the effort you putting in this channel.

Friederich Marcossy (3 years ago)

Find two vectors of norm 1 that are orthogonal to the three vectors u<2,1,-4,0> v<-1,-1,2,2> and w<3,2,5,4>

Phillip Le (3 years ago)

God

iEmbraceU (3 years ago)

Not all heroes wear capes

Lavender Oluoch (3 years ago)

my math saviour!

TripedalTroductions (3 years ago)

Are you subtracting j from i because they are on the same plane?

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