Cross Product of Two Vectors Explained!

This physics video tutorial explains how to find the cross product of two vectors (i, j, k) using matrices and determinants and how to confirm your answer using the dot product formula.
Introduction to Matrices: • Intro to Matrices
Adding and Subtracting Matrices:
• Adding and Subtracting...
Scalar Multiplication of Matrices:
• Scalar Multiplication ...
Solving Matrix Equations:
• Solving Matrix Equations
Multiplying Matrices:
• Multiplying Matrices
__________________________________
Gaussian Elimination & Row Echelon Form:
• Gaussian Elimination &...
Gauss Jordan Elimination:
• Gauss Jordan Eliminati...
Gaussian Elimination With 4 Variables:
• Gaussian Elimination W...
Inverse of a 2x2 Matrix:
• Inverse of a 2x2 Matrix
Inverse of a 3x3 Matrix:
• Inverse of a 3x3 Matrix
__________________________________
Determinant of 2x2 and 3x3 Matrix:
• Determinant of 3x3 Mat...
Determinant of 4x4 Matrix:
• How To Find The Determ...
Cramer's Rule - 2x2 Linear System:
• Cramer's Rule - 2x2 Li...
Cramer's Rule - 3x3 Linear System:
• Cramer's Rule - 3x3 Li...
___________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
Vectors - Free Formula Sheet:
bit.ly/3WYIGOv

[@TheOrganicChemistryTutor]

Vectors - Free Formula Sheet: bit.ly/3WYIGOv Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/pXzUpZqwZ8qiY7s

[@larrygilligan9070]

Not a college student here, just a senior citizen doing some good exercises for the mind. Good depiction, good narration, very good product. Thank you for putting this up on KZbin

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But still, there's physics lol

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[@raymondkyruana118]

@@kalebgarcia2733 Honestly, I would probably have gone CS or CE cause that's what a lot of us ended up doing anyways. Def worth the degree in terms of money, but there are other majors that make about the same if not more, with much better college experiences. I would say if you're just in it for the money (which is totally fine) then go finance/investment banking. You'll have a much happier college and probably life than forcing yourself to do this shit everyday. But if you actually like tedious problem solving and you like the challenge of tech (which isn't as glamorous as it seems haha) then yeah CS and EE/CE are worth it and you'll make solid money! Also Engineering management is a pretty good option too! Just make sure your GPA doesn't dip below 3-3.2 cause it's a lot harder to get a job right out of school! Not the end of the world cause eventually it doesn't matter but it can set you back for the first few years and makes getting a job less exciting from what I've seen:/ Good luck!!!

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[@hshshhs-ue7ef]

how you find J is negative and K is positive in first min

[@icanget9958]

@@hshshhs-ue7ef Because it's written as - J if we -5 (1--1) = -5 *+2 =-10 Hope it clears your doubt!

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[@stumblealongwithme]

How did you know the signs of i, j, and k?

[@thatgoose2639]

i is really i(11) which is row 1 column 1. the formula to find the sign is (-1)^(row # + column #) so i is (-1)^2 which is positive 1. For j, j(12) because it is in row 1 column 2. Apply the same formula (-1)^(1+2). (-1)^3 is -1, so you subtract. row k; K(1 3) row 1 column 3. apply the formula (-1)^(1+3). (-1)^4 =1. therefore you add. Most people just remember it goes i - j + k.

[@stumblealongwithme]

@@thatgoose2639 Thanks! That makes sense

[@ArsArcanum]

i was gonna ask the same. great explanation, Spider Rick

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Thanks!!!

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[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for another classic video selection and awesome explanation of the Cross Product of Two Vectors in Calculus Three. Cross Product is also introduced in Engineering Physics One, Statics and Dynamics. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

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We need teachers like You...

[@hshshhs-ue7ef]

how you find J is negative and K is positive in first min

[@calvin9388]

@@hshshhs-ue7ef organic chem tutor has a video on that too

[@calvin9388]

@@hshshhs-ue7ef "how to multiply matrices"

[@Cxore.58]

what if the a and b vector had different component? for example, a=3i+5j-7k and b=9m-2n+7p? And how do we get negative bc at 2:25? and I also didn't understand the minus on 3:01 and 3:16.

[@frenchlytical9438]

By Matrice rule, it is done that way..

[@samaabdelgelil210]

You are so good at explaining things simply and easily ..Thank you for your help.

[@brianadowning2904]

How did you get a negative in front of J and a positive in front of the k? Thank you for this video

[@amoghgaruda]

Just something to memorize. The proof behind it is not really necessary to know. (Usually. Your case might be different)

[@brianadowning2904]

@@amoghgaruda ok thank you!

[@johnnyboy6338]

It has to do with linear algebra and evaluating determinants larger than 2x2.

[@brianadowning2904]

@@johnnyboy6338 thank you!

[@lukaswalden6197]

If you want to have a positive in front of the J you could do the cross product with K in the left and I in the right side. Adding the negative just makes it easier to visualize without rewriting the I after K.

[@loaf8506]

thanks dude, i completely forgot everything from linear algebra! this is great for physics bc i don't have to find magnitudes and angles :)

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loaf 🍞

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Thank you so much! You explain far better than my physics teacher!

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I just sat through an hour and a half lecture about this and i understood this in 7 minutes from this vid

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soooooo helpful!!! I could not get this in 1.5 hours and you taught it in under 15 minutes.........

[@TechnologyWitch]

Your videos are the only thing keeping me afloat. Thank you so much!

[@-i2641]

how do we determine the signs between i,j and k? pls help

[@leozelenika8354]

true, just looking in the comments for exactly that

[@MarceloKatayama]

​@@leozelenika8354for three dimensions, it's just + - +

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Could you please upload videos on the following topics Vector spaces - Euclidean vector space, Vector subspaces, Linear combinations, Linear dependence and independence Applications of Vectors and Matrices - Plane transformations, Least squares Statistics - Data handling, Population vs Sample, Statistical parameters Statistics - Probability distributions: Binomial, Poisson and Normal distributions, Discussion of chi squared and Student t distributions. Statistics - Confidence intervals, Hypothesis tests; Level of significance, p- value, power of test

[@orbital16]

Im still confused, sorry. @1:44 does the signs are always the same in sequence as (+i) (-j) (+k)? Thanks..

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[@jonnafajardo956]

why does the j become negative and k is positive?

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Hi, you've been helping me with Calculus and was wondering if you are also teaching Linear Algebra because that class is killing me slowly and I really like your teachings.

[@Ultimate2T22]

Vectors are basically mentioned in pre calculus and calculus 3-4. So he is basically telling advanced linear algebra.

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@@Ultimate2T22 my algebra 2 teacher never taught me this and im in highschool currently and im going to take AP calculus in 2 months but Im currently taking Pre-Calc and they mentioned vectors and cross product method so im watching this video.

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how funny that i only learn in this channel. and never in class. what a waste of time

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Yeah

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[@TheJayaldae]

Why was it -j but +k?

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thank you for teaching the one topic and lesson i hate the most. u made this so easy to remmebr and learn

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[@SizolwethuMasimula-nr2jx]

Why is j negative

[@DiliniMaduwanthi-xn1xi]

Consider that is matrix 1st column is positive 2nd column is negative and 3rd column is positive

[@ka1serrrrr]

​@@DiliniMaduwanthi-xn1xi Why is the 2nd column negative I don't get it

[@DiliniMaduwanthi-xn1xi]

Please refer a 3x3 matrix video

[@chibles1756]

@@ka1serrrrr In Maths 101 matrices you learn about Co-Factor Expansion and it basically States a general formula as: i(-1)^Row+Column +j(-1)^Row+Column + k(-1)^Row+Column Obviously with the respective 2x2 Matrix next to i,j,k But the row and column shows 1+1, 1+2, 1+3. now obviously when you raise -1 to a even power it results in a + and when raised to an Odd number it remains a -1 this now determines whether it is a + or a Minus

[@ka1serrrrr]

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[@oddst]

After you make the new matrices, why is it i - j + k? Is the j always negative?

[@sbp___9865]

do you mean j is always negative? I'm still confused on this.

[@oddst]

@@sbp___9865 yeah j, sorry

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[@y3ll0ch0c0lat3]

Can someone explain why in the first example, J is negative but K is not?

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I have the EXACT SAME QUESTION!!!

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[@medicisounds1384]

Why is it "minus" J and not plus?

[@priyashrivastav239]

there are some rules behind it..according to which the elements of matrix a11 a12 a13 a21 a22 a23 a31 a32 a33 so when we find the determinant of them the elements which has the sum of aij as odd will get negative sign and those which have even sum for aij will get positive sign during determinants.

[@erickarwa-0705]

Throughout 5 years of undergrad studies in engineering, I never knew vector cross product is this simple! Eish!

[@willardmakinishi6980]

I have gained a lot of understanding from your explanations NOT just on this topic but across multiple topics or courses and its not something I take for granted. I am and I will forever be grateful for that. I have a bit of a challenge to understand where the negative is coming from on in the component i (-4 3) ( 2 -8 ) for me I am getting a 38 after cross multiplying -4*(-8) =32 and 2*3=6. hence 32+6 =38. where is the 32-6 coming from? Secondly, where is the Negative coming from j. I have seen you are adding the i and k components but on the j you are subtracting or negating?

[@codyhenry2037]

I am also confused about why we are subtracting the j

[@alberttembo4357]

Very good! Well explained

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Your videos are pure gold 5*

[@muhammadhashimbinquraish7802]

Question 2:20 Why is " j " negative and " k " positive? Is there a reason or we must always do it like this?

[@LiveAventura]

Muhammad Hashim Bin Quraish the original equation has a negative sign on the j (i-j+k ). Look at the sign in front of the letter in the equation

[@Christine-wi5us]

there's actually a sign convention that you should follow, when you're looking for the determinant of a 3x3 matrix

[@lunarz7117]

As @That Goose comented earlier:- i is really i(11) which is row 1 column 1. the formula to find the sign is (-1)^(row # + column #) so i is (-1)^2 which is positive 1. For j, j(12) because it is in row 1 column 2. Apply the same formula (-1)^(1+2). (-1)^3 is -1, so you subtract. row k; K(1 3) row 1 column 3. apply the formula (-1)^(1+3). (-1)^4 =1. therefore you add. Most people just remember it goes i - j + k.

[@Vedant.Dhawan]

(-)(-)(-)=negative

[@bob_rcp49]

It is just a deduction but I want u 2 confirm it and tell me if I am right or not..... u r an Egyptian , your age = [16,18] , u r from STEM schools in either 11th or 12th grade this all could be wrong but this is just a deduction when it comes to ur question , u have to study matrices (matrix) before studying cross product so that u can understand well how is it like that

[@josephjoseph5874]

Thank you so much man. Literally a life saver.

[@wr6790]

Bro I had to comment, saw this problem on one of my quizzes had no idea had to start, but thank's to you I understand now

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Thank you for teaching me something new.

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thanks organic tutor you the reason where i'm. MORE LIFE

[@Wappeee]

10:06 Why is it minus j :( im kinda lost

[@azwadbinarif783]

It minus j cause we follow the rule for co-factors in determinant value. Formula is (-1)^ i+j where i and j are row and column no. Respectively. Or as a shortcut you can say if the addition of i+j is even we put + and if its odd we use minus !!

[@ashmi-ratatata3944]

@@azwadbinarif783 thanksssss

[@mdjunaedhossain409]

Best edu channel ever

[@goodsonnyirongo8970]

You are naturally gifted Man ✍️✍️✍️✍️✍️✍️ thanks for giving me such full data on vector product (cross product) and scalar product (dot product)🙏🙏🙏🙏🙏🙏

[@levikroeker7133]

👾

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Thank you so much. I am terribly grateful for this channel.

[@shireenkhan6847]

I'm so close to failing cal, and you seem to be my only ray of light

[@manuboker1]

Great math lesson!!! Thanks

[@supercorn5607]

1:27 Why is it -j? Please answer :(

[@manurajrauniyarrr]

Exactly

[@jeraldshau6187]

It's cofactor is - remember that thing where it's alternates​@@manurajrauniyarrr

[@BushraAsad-x2o]

Study the chapter derterminant

[@BushraAsad-x2o]

In 3×3 matrices the signs are [+ -+ - + - + -+]

[@elliotpostma7718]

What about when you just have i and j, no k? Why negative j and positive k in the first example?

[@tsowane]

Thank you so much man, you're my hero

[@hamdial-akkad8339]

Thank you a lot u made my day it's like playing a game with its passwords

[@Boomer129]

Pls, can you explain the sign convention for the three vectors

[@zeemusty5762]

5years ago and still helpful

[@moseschansa5666]

Excellent Lesson .Good

[@JovialGola]

This is beyond teaching 😊😊

[@malakasadalikhan109]

1:45 Cross Product Formula 4:10Check (5:20,7:15) 9:00

[@quixQuery]

There's too many positive comments here so I thought I'd share my perspective lol. I watched this video for a couple minutes, and didn't understand what was going on at all. Then I went to the first webpage in a google search for "Cross product explained" and understood it conceptually within 2 minutes. I'm glad this video helped some people though, power to them! (And great on the guy posting it!) It did not help me though.

[@Noahmalacad]

I love your teaching skills bro.

[@hshshhs-ue7ef]

how you find J is negative and K is positive in first min

[@naynayngwens]

Thanks! Really appreciate the help.

[@WilliamsBoakye-ko4ho]

Thank you boss. May God bless you

[@annahosea4437]

Thank you for the video I have gained more

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