*Spends hour and half in class confused* *Goes to hour of lab the next day slightly less confused but still very lost* *Goes home and watches 10 minute video on TH-cam* Ohhhhhhh, that's what's going on!
Khan Academy Shouldn’t the (-24-21) actually be (-24+21)? I’m not sure where the -7 is coming from in the “i” calculation. Just seems strange that I didn’t see another comment on this...
For determinants I found a quicker method in a physics books from the 80's when I was studying. It amounts to the same thing but doesn't use sub determinants. You start at row 1, and scan right (additions) and diagonally down. So the first vector would be i * -6 * 4, then j * 3 * -2 [note that you always wrap around regardless of direction] and then k * 5 * 7. Then you repeat in the for the subtractions going from right to left, -(i * 3 * 7) -(k * -6 * -2) -(j * 5 * 4). You then sum it all up. It makes rapid work of calculating a determinant as you can scan and calculate each component and write it down and then just do a final addition. Alternatively you can zig right on "i" and then -zag left on "i" and get the i component in one pass. This technique is especially useful for large matrices because you don't have to constantly decompose to 2x2's. I see that the method I learned is called the "Diagonal Method". It stuck with me!!
Khan Academy There is a much easier way to do the cross product than demonstrated in this video. What one can do is create an array with the first column, from top to bottom, reading i, j, k. Then list the numbers of the first vector in the second column, then the second vectors in the third column, then i, j, k again, then the first vector's numbers again, making a total of 5 columns. Then draw lines through all the diagonals with 3 numbers in them (make an arrow at the end of line pointing towards the bottom). Multiply all the stuff in each diagonal and write it at the bottom. The first 3 terms are multiplied by -1 and the last 3 are summed. This makes it easier to see what is happening in the operation.
He mentioned he sometimes makes careless mistakes. That's pretty normal. That's why double checking your work is so important. I wish someone would have that talk with Sal Khan... Lol
wow, thank you, this was never explained in my physics class in university, they just kind of expected you to already know this!!! You just saved me on my homework!!!
So even if we are given the engineering format of the vectors WITH feta, we should opt not to use the cosine function but rather just multiply the vectors components respectively because it is much easier.
After 117 videos of this physics playlist, I have to thank you. It helped a lot to understand the mechanics, statics and kinematics. Also the videos about fluids were really useful for me.
after i watched this video Calculating the dot and cross products when vectors are presented in their x, y, and z (or i,j, and k) components., my insight is very open because the video is very good to give information
@khanacademy no khan you are really great u taught me though..............and hazarat ALI says whoever taught u even a word is ur teacher but u taght me so much so you are my teacher.....!!!!!!!!!!!!!!!!!!!!!!!!!!!!
did you find graphing software? I would love to be able to visualise all there things so I can wrap my head around what's going in in space. If possible, vectors, planes, + more Thanks
Thank you. Well explained and understood. I apologize, on the cross product of the I component we have an error of addition. Nothing to do with the process. Again, thank you!
How would you find the direction for the cross product result? I just can't see or grasp the idea of a 4th dimension that would be perpendicular to all three dimensions..
Great video, thanks. One thing I find difficult is the direction of the x product when starting with three dimentional vectors. How do you visualise something that's perpendicular to a three dimentional space?
Great video however I'm a little confused as to why it's +, -, + instead of +, +, + at 6:46 mark. Can anyone help me understand the reasoning of adding and or subtracting?
The formula for the sign is equal to (-1) ^(i+j). , so for example you are taking the minor of row 1 colum 2 , your i=1 and your j =2, the sign would be equal to (-1) ^(1+2) that is (-1)^3 , that is why you have a negative sign on row 1 column 2. In other words , if the sum of your row and column is odd , the sign is negative, if it is even the sign is positive. Shortcut is label it like a checker board, starting on the upper left corner with a positive, then just alternate the signs. Hope this helps.
How could a magnitude be worked out using the dot product method if vectors a and b are inconsistent? For example vector a = (3.0i - 4.0j) and vector b = (-2.0i + 3.0k). I was told to expand these using the distributive law, however, that's not what Sal does in this video...
i vector should be |-6 3| |7 4| which means i vector should be (-24 + 21)i The J is correct. & shouldn't k be (35+12)k since a (-) times a (-) is a (+)? The answer I got was -3i (-26j) +47k. Correct me if I'm wrong. @Khan Academy could you please verify this thanks.
i am not able to understand that which sign is will we use and when can u make a vidio on more such cross products pradeeps que to under stand it more clearly
i think the cross product calculations made were wrong....even after the -45i mistake...there was another right after ...instead of taking {(3.-2)-(5.4)},which equals -26,... u did the reverse...meaning 20-(-6)...resulting in +26. After doing it both ways and checking your solution for a perpendicular cross product of zero by (-45i,26j,23k) x (5,-6,3) u will find that using +26 does not result in 0 but rather gives an answer of -312 ....even after using -45i, whereas using -26 produces zero
Ok, if I do the dot product by your algorithm for and I get (1*2)+(2*1) + (0*0) = 2 + 2 = 4. But the projection of onto doesn't have length 4; it's much shorter than that. What am I missing.
The dot product is the length of the projection |projb a|, not the projection itself. The projection (projb a) is actually another vector. It's defined thusly: projb a= [(a•b)/(b•b)]*b The [(a•b)/(b•b)] make a scalar value, which you then multiply by b.
for all those watching this videos....how old are you guys?? i mean iam 15 in class 11th and studying this for college entrance exam{IIT}(2 years later)
![ค้าง (STILL) - GEMINI [ OFFICIAL MV ]](http://i.ytimg.com/vi/Ftxx3hk5vkU/mqdefault.jpg)
as a 29 yr old struggling to make it through engineering, this type of instruction is invaluable to me. Thank you so much.
Now you must be 39 years of old btw now are you working in a job Or something else??
How are you doing now?
why did u comment this
How are you?
*Spends hour and half in class confused*
*Goes to hour of lab the next day slightly less confused but still very lost*
*Goes home and watches 10 minute video on TH-cam* Ohhhhhhh, that's what's going on!
You kids are lucky this stuff exists. Back in the day we had to learn things the hard way.
And I do consider myself lucky. This is great material, especially if you understand most but not quite all, or just need a quick review for a test
AuroraBorealis5030 literally me
My bad. Need to learn to add/subtract.
Khan Academy
Shouldn’t the (-24-21) actually be (-24+21)? I’m not sure where the -7 is coming from in the “i” calculation. Just seems strange that I didn’t see another comment on this...
no, u r great, that was a typo
@S. I. V. that's what he means it shouldnt be negative
@S. I. V. ohhh we were both confused we didnt realise you need to subrtact one from the other, not add
Not sure if it's been brought up. For the answer I got -45j -26j +23k
its the correct answer
Its actually 18k
no i think u did 5 X 6 instead of 5 X 7
thats the correct answer
It's not 18k coz it's 35-12 not 35-17
For determinants I found a quicker method in a physics books from the 80's when I was studying. It amounts to the same thing but doesn't use sub determinants. You start at row 1, and scan right (additions) and diagonally down. So the first vector would be i * -6 * 4, then j * 3 * -2 [note that you always wrap around regardless of direction] and then k * 5 * 7. Then you repeat in the for the subtractions going from right to left, -(i * 3 * 7) -(k * -6 * -2) -(j * 5 * 4). You then sum it all up. It makes rapid work of calculating a determinant as you can scan and calculate each component and write it down and then just do a final addition. Alternatively you can zig right on "i" and then -zag left on "i" and get the i component in one pass. This technique is especially useful for large matrices because you don't have to constantly decompose to 2x2's. I see that the method I learned is called the "Diagonal Method". It stuck with me!!
The answer should be -45i^ -26j^ +23k^
Khan Academy There is a much easier way to do the cross product than demonstrated in this video.
What one can do is create an array with the first column, from top to bottom, reading i, j, k. Then list the numbers of the first vector in the second column, then the second vectors in the third column, then i, j, k again, then the first vector's numbers again, making a total of 5 columns. Then draw lines through all the diagonals with 3 numbers in them (make an arrow at the end of line pointing towards the bottom). Multiply all the stuff in each diagonal and write it at the bottom. The first 3 terms are multiplied by -1 and the last 3 are summed. This makes it easier to see what is happening in the operation.
yeah did you see hat one video aswell
Dot product 3:10
Cross product 5:20
Thanks bud
Sal, you're a saviour mate. Got my LA exam tomorrow in computer science and these vids are golden. Your gift to the public is truelly appreciated.
How did your exam go ?
I swear khan academy videos are getting me through Uni
grennyfell97 same here bud
really?
Yep, professors love running
Why am I getting notifications over a year later?
+grennyfell97 by chance
Well explained, and with enthusiasm.
-45i though.
Oi ! . I am from 2023. Hows life ? U alive right ? 😃
so basically you don't need to be good at math to be good at math......
He mentioned he sometimes makes careless mistakes. That's pretty normal. That's why double checking your work is so important. I wish someone would have that talk with Sal Khan... Lol
wow, thank you, this was never explained in my physics class in university, they just kind of expected you to already know this!!! You just saved me on my homework!!!
So even if we are given the engineering format of the vectors WITH feta, we should opt not to use the cosine function but rather just multiply the vectors components respectively because it is much easier.
After 117 videos of this physics playlist, I have to thank you. It helped a lot to understand the mechanics, statics and kinematics. Also the videos about fluids were really useful for me.
after i watched this video Calculating the dot and cross products when vectors are presented in their x, y, and z (or i,j, and k) components., my insight is very open because the video is very good to give information
Now i have started taking studies as a part of playing cool games,its really awesome.Thanks SAL.
Thanks, you explained that process so well. You're an excellent teacher Mr Khan.
Dang hi you left this comment 12 years ago
@khanacademy no khan you are really great u taught me though..............and hazarat ALI says whoever taught u even a word is ur teacher but u taght me so much so you are my teacher.....!!!!!!!!!!!!!!!!!!!!!!!!!!!!
did you find graphing software? I would love to be able to visualise all there things so I can wrap my head around what's going in in space. If possible, vectors, planes, + more
Thanks
ah... -21-24=-45....
also 35-17 = 18
@@senatorpoopypants7182 it's -6×-2 is 12, his handwriting just makes it look like it's 17
you sir have helped me pass my linear algebra test......you are truly amazing thank you!!!
Classes of 3 Days Physics Done in 10min not to mention it's clearer here
Awesome tutorial thanks!
thanks. never thought this would be so easy for both operations.
Thank you. Well explained and understood. I apologize, on the cross product of the I component we have an error of addition. Nothing to do with the process. Again, thank you!
Hey
really helps me with my computer graphics ! thanks !
Haha, the -45 not -35 threw me off. Spent 5 minutes trying to figure out what I did wrong. Great video regardless.
Best teacher ever
I joined my linear algebra class 2 weeks late, even my prof told me to come watch Kahn academy to get caught up 😂
Khan sir ur vedios r simply awesome ....☝👍👍
Splendid! Perfect definitions of both dot and cross product
Cross product starts from 4:98
great explanation.. I did search for hours to understand this.
You got my sub sir.
Excellent video , thank you so much.
i would really like to practice this at Khan Academy!! :D thanks anyway! great explanation!
thanks it helped me a lot
Thank you so much !!
this was great..thank you so much
How would you find the direction for the cross product result? I just can't see or grasp the idea of a 4th dimension that would be perpendicular to all three dimensions..
Tq brooo... Very much helpfull👍👍👌👏💜💜💜
Adding/Subtracting is the hardest part of Calulus/Physics.
7m,9kn vector is I and j 3m,6m,7m
What is your answer
Hello 😃.
Its been 14 years . Are you still alive ?. What are you doing now ?
Great video, thanks. One thing I find difficult is the direction of the x product when starting with three dimentional vectors. How do you visualise something that's perpendicular to a three dimentional space?
helpful! Thx!
how do you find the cross product of just 2 determinants
Great video however I'm a little confused as to why it's +, -, + instead of +, +, + at 6:46 mark. Can anyone help me understand the reasoning of adding and or subtracting?
I have the same question
Let me know when you figure it out :) I moved onto my Chemestry course; I will return to this later.
The formula for the sign is equal to (-1) ^(i+j). , so for example you are taking the minor of row 1 colum 2 , your i=1 and your j =2, the sign would be equal to (-1) ^(1+2) that is (-1)^3 , that is why you have a negative sign on row 1 column 2. In other words , if the sum of your row and column is odd , the sign is negative, if it is even the sign is positive. Shortcut is label it like a checker board, starting on the upper left corner with a positive, then just alternate the signs. Hope this helps.
thx alot. it make me recall alot of thing for my exam.
How did your exam go 😃?
I love you. =D Literally, you're speaking my language.
r u alive?
@@elonmusk8102 yes 😂😂.this my new channel
8:50 the k vector component should be (35+12) therefore 47k
helped so much for my test tm, cant thank you enough
Did you pass ?
Thanku so much sar muje samje hi nahi aa raha tha aapka video dakh kar Mai bahut ache se samaj gaye sar thanku so much
Thank you so much
Thanks!
Thanks👍😊
Take the coefficient of 'k'as 0!
Did that help?
How could a magnitude be worked out using the dot product method if vectors a and b are inconsistent? For example vector a = (3.0i - 4.0j) and vector b = (-2.0i + 3.0k).
I was told to expand these using the distributive law, however, that's not what Sal does in this video...
8:44 -21-25 equals -45
Thanks Sir
Where did the cos theta go?
i vector should be |-6 3|
|7 4|
which means i vector should be (-24 + 21)i
The J is correct.
& shouldn't k be (35+12)k since a (-) times a (-) is a (+)?
The answer I got was -3i (-26j) +47k. Correct me if I'm wrong.
@Khan Academy could you please verify this thanks.
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thank you
IM SORRY BUT THE CROSS PRODUCT U HAVE DONE IS WRONG it shhould be -45i-26j+23k
instead of -35i-26j+23k Thanks
Great video
ENGINEERING NOTATION GAH SO COOLL ☺️☺️☺️
thanks
Absolute value of vector a and vector b times cosine( or sine) of angle is not relevant in this video? Or is it? How?
I assume a(dot)b is negative 40 because the angle between them is greater than 90 degree, correct?
was it so hard for my textbook and teacher to just put it like that?
No, you were correct, -40 is the right answer for the dot product.
Oi , you alive . I am from 2023 . 😃
How do you find add and sub signs in between subderminant products in colross product
itwas very helpful
When doing the Cross product vector i should be -45 not -35!!
The answer for 1 question -10i^ - 42j^ + 12k^. Not 40
Geogebra has a 1/2 decent 3d graphing calc...but i am waiting for desmos to realise one...its so much more better than geogebra
good explanation, thanks. Is it a x b = -45i -26j +18k
8:33 should be -45 not -36
@nupsyyy Same here! :D
Is there an error in this video? @ 8:17 he says -24-21 = -35 but that's not correct or am i missing something?
@khanacademy no no. you're good :D
" -45 "
:3
Mr. Khan, do you do one-on-one online tutoring via Teamviewer? -Paid options are fine, of course.
super
i am not able to understand that which sign is will we use and when can u make a vidio on more such cross products pradeeps que to under stand it more clearly
i think the cross product calculations made were wrong....even after the -45i mistake...there was another right after ...instead of taking {(3.-2)-(5.4)},which equals -26,... u did the reverse...meaning 20-(-6)...resulting in +26. After doing it both ways and checking your solution for a perpendicular cross product of zero by (-45i,26j,23k) x (5,-6,3) u will find that using +26 does not result in 0 but rather gives an answer of -312 ....even after using -45i, whereas using -26 produces zero
Oi , you alive. Hows life . I am from 2023 😃
Did you prove vector product is distributive?, I found a way to prove it but I'm looking for a more elegant proof...
Theirs some error in 8: 35
Where u said (-24-21) = 35 and it's wrong ❌ it's minus 45. Anyways thanks 😌🙏.
Ok, if I do the dot product by your algorithm for and I get (1*2)+(2*1) + (0*0) = 2 + 2 = 4. But the projection of onto doesn't have length 4; it's much shorter than that. What am I missing.
The dot product is the length of the projection
|projb a|,
not the projection itself. The projection (projb a) is actually another vector. It's defined thusly:
projb a= [(a•b)/(b•b)]*b
The [(a•b)/(b•b)] make a scalar value, which you then multiply by b.
Is there any other way to find vector product other than Matrix method?? I mean using Sine formula..
which software did he use for writing ,its really funcy 1 , anybody help here
Oi , its been 14 years . You still alive . Hows life 😃
@manmaba here too xD
this silly calculation mistake
-45i not -35i
There's an error in calculation
Pliz show how to prove
you made a calculation mistake (-24-21) ... Thx for the video
-24-21=-45 sir not-35
for all those watching this videos....how old are you guys??
i mean iam 15 in class 11th and studying this for college entrance exam{IIT}(2 years later)
How do you do this in 2D?
How to do cross product in 2/2matrix
-45i not -35I
Cross product of vectors (in i j components) in 2D anyone?
-45i