This video is priceless!!! I've struggled for hours with my copy of "3D Math Primer" book trying to understand what cross product is really about and then I've found your video and BOOM! I've got it! Thank you so much for your help!
Sal sums its up at the end like a BOSS. "You use your right hand, point in like gun, make all your fingers perpendicular and then you'll know what direction that vector points in."
another method is moving your index finger from the first vector to the second. if your index finger moves to the left, it is coming out of the screen, like a screw, if it moves to the right, it is going into the screen. righty tighty, lefty loosey. i believe it is called the screwdriver rule.
It's a convention. Elsewhere, when using hands to distinguish cartesian co-ordinate systems, X is the thumb, Y is the first finger and Z is the middle finger.
Thats right, "axb" and "bxa" are along the same line, they're just in exactly opposite directions. Imagine drawing the vectors a and b on the ground, and then sticking a pole in the ground where they meet. axb would be the vector along that pole pointing towards the center of the earth, while bxa would be the vector along the pole pointing towards the sky.
In Ukraine there is a left hand rule, which i find much easier actually. At least, because you can write and perform the rule at the same time. And, in my opinion it`s easier to understand and do (the a is the pointing finger and b goes into your palm).
This is good, but when you are trying to build intuition, you could just say that the magnitude of the cross product is equal to the area of the parallelogram implied by vectors 'a' and 'b'.
ur right =p im taking calc 3 and general physics, and both of them will teach dot/cross product in the beginning. so i dont have that prob, but i guess most engineering students will learn dot/cross in physics first
They didn't choose the right hand out of convention--they chose the right hand because they found, experimentally, that that direction scheme displayed on the right hand comported with the physics data as opposed to the left hand. It wasn't because there are more right-handed people than left-handed people or something like that.
'a x b' and 'b x a' are both cross products which are perpendicular to a and b respectively. does this mean that, if you have two vectors (a and b) there is more than one vector that is perpendicular to both a and b? ('a x b' and 'b x a'?) how is this so?
Never thought I'd find gang signs in a math tutorial! :D BTW, my book describes the RRR differently. You base the orientation of the cross product on the direction the fingers curl... Confusing as heck...
It is repeatedly being said that you have to consider the smaller angle. When you r saying the angle is 100 degrees, this means that you are placing the vectors incorrectly. So place them correctly and then the angle between the vectors will be 80 degrees and you can further solve the whole problem Hoping that u get it
wait i think i get it. both 'a x b' and 'b x a' are along the same 'line', if you will. it's just that their directions are opposite? using the right-hand rule and flipping it round it seems that way...
Is it just me or does anybody else realize that Mr. Sal discussed Fleming's left hand rule but he called it the right hand rule???? BTW in my opinion this is too much math. xD
"If we were metal filings living in a strong magnetic field we'd probably have a better intuition of this" lol!
the most impressive things about these videos is his right hand rule drawings....gives a nice visual...thanks.
This video is priceless!!! I've struggled for hours with my copy of "3D Math Primer" book trying to understand what cross product is really about and then I've found your video and BOOM! I've got it! Thank you so much for your help!
Sal sums its up at the end like a BOSS. "You use your right hand, point in like gun, make all your fingers perpendicular and then you'll know what direction that vector points in."
you're instantly and permanently my favorite person.
Is he still your favourite person ?
another method is moving your index finger from the first vector to the second. if your index finger moves to the left, it is coming out of the screen, like a screw, if it moves to the right, it is going into the screen. righty tighty, lefty loosey. i believe it is called the screwdriver rule.
It's a convention. Elsewhere, when using hands to distinguish cartesian co-ordinate systems, X is the thumb, Y is the first finger and Z is the middle finger.
Thats right, "axb" and "bxa" are along the same line, they're just in exactly opposite directions. Imagine drawing the vectors a and b on the ground, and then sticking a pole in the ground where they meet. axb would be the vector along that pole pointing towards the center of the earth, while bxa would be the vector along the pole pointing towards the sky.
Wahhh!!! U truly deserve appreciation for your efforts and hard work.
Hahaha moments like 2:08 make me not stop loving you!
By far the best tutorials on internet!
can u imagine how frustrating this must be for right hand amputees
they have to do inverse right hand rule on left hand
It wouldn't be that hard though... i think they would just have do the left hand rule and know the answer will be the opposite direction
In Ukraine there is a left hand rule, which i find much easier actually. At least, because you can write and perform the rule at the same time. And, in my opinion it`s easier to understand and do (the a is the pointing finger and b goes into your palm).
Thank you.. For the first time I understand what vector cross means
"Your index gets the first term, the middle finger gets the second term". Finally I get it. THANK YOU!
U r an artist with science I HV ever seen
This is good, but when you are trying to build intuition, you could just say that the magnitude of the cross product is equal to the area of the parallelogram implied by vectors 'a' and 'b'.
I've encountered this before in Calc III but it was NEVER THIS CLEAR.
ur right =p im taking calc 3 and general physics, and both of them will teach dot/cross product in the beginning. so i dont have that prob, but i guess most engineering students will learn dot/cross in physics first
Tq khan,may God bless u
They didn't choose the right hand out of convention--they chose the right hand because they found, experimentally, that that direction scheme displayed on the right hand comported with the physics data as opposed to the left hand. It wasn't because there are more right-handed people than left-handed people or something like that.
Most fond childhood memory, playing with water lol.
Yeah, I agree 3D Math primer seems to glaze over dot and cross products.
Excellent video. Thank you.
@thebutleress
Because if you do so, you would get an opposit result..
Left hand rules are only used (as far as I know) for a Lorentz force.
'a x b' and 'b x a' are both cross products which are perpendicular to a and b respectively. does this mean that, if you have two vectors (a and b) there is more than one vector that is perpendicular to both a and b? ('a x b' and 'b x a'?) how is this so?
I find the alternative right hand rule way easier to actually do. You can find a video on youtube describing.
Here the right hand rule can be applied only if the two vectors are orthogonal .. but in this case it's 30deg does it makes no difference???
Never thought I'd find gang signs in a math tutorial! :D
BTW, my book describes the RRR differently. You base the orientation of the cross product on the direction the fingers curl... Confusing as heck...
aweasome video really helped a lot
very helpful..hatur nuhun
Great vid. Thank you. But what if the angle between a and b was something like 100 degrees, where there could be no right angle onto b?
It is repeatedly being said that you have to consider the smaller angle. When you r saying the angle is 100 degrees, this means that you are placing the vectors incorrectly. So place them correctly and then the angle between the vectors will be 80 degrees and you can further solve the whole problem
Hoping that u get it
thank you very much... its a great help...
I got exactly what i wanted. thanks
wait i think i get it. both 'a x b' and 'b x a' are along the same 'line', if you will. it's just that their directions are opposite? using the right-hand rule and flipping it round it seems that way...
It must be. At least, I've encountered it only in Lin Alg class this far.
he is an artist.
thank you khan, your videos are really helpful!! my lecture in university makes me sleep, but you dont ^^
Same here
This is really helpful thanks!
wait... so how do I calculate for cross product with 2 vectors again?
Why does cross product give a vector which is perpendicular to a plane?
You're brilliant!
You are the best !!!!!!!!!!!!!!!!!!
a bundel of thankssssssssssssssssss khan we love u
Tnk u very much
nice video very helpful
thank you for making this
awesome explanation.... :)
why is Right Hand Rule used and not Left hand rule?
Really nice art skills
Woah Kahn, maybe you've played with water..
@marcunator thanks :)
how can vectors point of of a page when they are multiplied? I can't visualize this.
Dont think of the cross product as multiplication
Is this a linear algebra topic?
“Let me redraw it”
.... what if we didn’t let him redraw it? 🤔
confused... i just tortured my hands trying to understand this
may GOD bless to who make this video...^_^
Is it just me or does anybody else realize that Mr. Sal discussed Fleming's left hand rule but he called it the right hand rule????
BTW in my opinion this is too much math. xD
I dont get the right hand rule. My thumb stays the same xd. Can someone explain ?
Person status: Favourite.
My thumb goes down both times, should I go to the Doctor?
You're not the only one. My thumb doesn't even change.