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.
Vectors - Free Formula Sheet: bit.ly/3WYIGOv
_______________________________
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

[@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

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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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[@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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[@MrJensenMath10]

If you're looking for a good visual demonstration of cross product and the right hand rule check out my explanation at kzbin.info/www/bejne/sHPIYZuwaZWYipY

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[@09110G]

Anyone comming here just before exam because lost in vector product 🤧🤣

[@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

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@@hshshhs-ue7ef "how to multiply matrices"

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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

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

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u explain things in 10 mins that my lecturers cant in whole semester @goat

[@Bearded_Dragon_Sir]

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

[@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.

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

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[@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..

[@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.

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You are a true genius, thank you for your help!

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

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

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

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5years ago and still helpful

[@ClancyFinn]

Why is it -j? 1:35

[@guitarttimman]

You should also explain that the Cross Product does not follow the commutative property.

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thank you for this video!!! got a little triggered by the vectors not having arrows above them but hey! can't get everything in life. lmao. Thanks again =)

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Blessed KZbinr

[@-i2641]

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

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true, just looking in the comments for exactly that

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

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i like to repeat 00:32 idk why but it makes a lit beat

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God bless you Mr JG

[@ferangiznutfullayeva3018]

I found it really helpful. Also I have question In multiplying 3×3 matrix how u know it is negetive or positive between i j k

[@hshshhs-ue7ef]

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

[@duskiiiyy4872]

@@hshshhs-ue7ef just a rule guys, its always negative before the j :)

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Great video,Im leaving a comment to help u out

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Great math lesson!!! Thanks

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Excellent video sir