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.
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...
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.
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'.
'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?
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).
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 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
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
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!
the most impressive things about these videos is his right hand rule drawings....gives a nice visual...thanks.
"If we were metal filings living in a strong magnetic field we'd probably have a better intuition of this" lol!
you're instantly and permanently my favorite person.
Is he still your favourite person ?
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."
Wahhh!!! U truly deserve appreciation for your efforts and hard work.
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.
U r an artist with science I HV ever seen
Thank you.. For the first time I understand what vector cross means
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.
Hahaha moments like 2:08 make me not stop loving you!
By far the best tutorials on internet!
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...
Tq khan,may God bless u
I've encountered this before in Calc III but it was NEVER THIS CLEAR.
he is an artist.
thank you very much... its a great help...
I got exactly what i wanted. thanks
Excellent video. Thank you.
aweasome video really helped a lot
very helpful..hatur nuhun
This is really helpful thanks!
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
"Your index gets the first term, the middle finger gets the second term". Finally I get it. THANK YOU!
You're brilliant!
You are the best !!!!!!!!!!!!!!!!!!
thank you khan, your videos are really helpful!! my lecture in university makes me sleep, but you dont ^^
Same here
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.
thank you for making this
Yeah, I agree 3D Math primer seems to glaze over dot and cross products.
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 find the alternative right hand rule way easier to actually do. You can find a video on youtube describing.
'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?
Tnk u very much
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).
awesome explanation.... :)
Most fond childhood memory, playing with water lol.
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...
nice video very helpful
@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 bundel of thankssssssssssssssssss khan we love u
wait... so how do I calculate for cross product with 2 vectors again?
Really nice art skills
It must be. At least, I've encountered it only in Lin Alg class this far.
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
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???
Why does cross product give a vector which is perpendicular to a plane?
why is Right Hand Rule used and not Left hand rule?
“Let me redraw it”
.... what if we didn’t let him redraw it? 🤔
confused... i just tortured my hands trying to understand this
Is this a linear algebra topic?
@marcunator thanks :)
may GOD bless to who make this video...^_^
Woah Kahn, maybe you've played with water..
Person status: Favourite.
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 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 ?
My thumb goes down both times, should I go to the Doctor?
You're not the only one. My thumb doesn't even change.