Cross Product of Two Vectors Explained!
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- Опубліковано 25 сер 2024
- 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
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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 Formula Sheet:
bit.ly/3WYIGOv
Vectors 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: ua-cam.com/video/oKqtgz2eo-Y/v-deo.html
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how you find J is negative and K is positive in first min
@@hshshhs-ue7ef Because it's written as - J
if we -5 (1--1)
= -5 *+2
=-10
Hope it clears your doubt!
Crazy how you carried my all through high school and now I’m in college still watching
If you're looking for a good visual demonstration of cross product and the right hand rule check out my explanation at ua-cam.com/video/zBe0hz40eT4/v-deo.html
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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 UA-cam TV with the Organic Chemistry Tutor.
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How did you know the signs of i, j, and k?
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.
@@thatgoose2639 Thanks! That makes sense
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how you find J is negative and K is positive in first min
@@hshshhs-ue7ef organic chem tutor has a video on that too
@@hshshhs-ue7ef "how to multiply matrices"
why does the j become negative and k is positive?
Thank you so much! You explain far better than my physics teacher!
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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How did you get a negative in front of J and a positive in front of the k? Thank you for this video
Just something to memorize. The proof behind it is not really necessary to know. (Usually. Your case might be different)
@@amoghgaruda ok thank you!
It has to do with linear algebra and evaluating determinants larger than 2x2.
@@johnnyboy6338 thank you!
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.
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.
By Matrice rule, it is done that way..
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Yeah
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how do we determine the signs between i,j and k? pls help
true, just looking in the comments for exactly that
@@leozelenika8354for three dimensions, it's just + - +
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Statistics - Confidence intervals, Hypothesis tests; Level of significance, p- value, power of test
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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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Why is j negative
Consider that is matrix 1st column is positive 2nd column is negative and 3rd column is positive
@@DiliniMaduwanthi-xn1xi Why is the 2nd column negative I don't get it
Please refer a 3x3 matrix video
@@MoonKaiser 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
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Im still confused, sorry. @1:44 does the signs are always the same in sequence as (+i) (-j) (+k)? Thanks..
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Why is it "minus" J and not plus?
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.
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After you make the new matrices, why is it i - j + k? Is the j always negative?
do you mean j is always negative? I'm still confused on this.
@@sbp___9865 yeah j, sorry
this way is way quicker , i dont y my teacher is making me solve equations simultaneously
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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 =)
5years ago and still helpful
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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?
I am also confused about why we are subtracting the j
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10:06 Why is it minus j :( im kinda lost
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 !!
@@azwadbinarif783 thanksssss
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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What a clarified idea!
Can someone explain why in the first example, J is negative but K is not?
I have the EXACT SAME QUESTION!!!
0:32
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Thank you for the video I have gained more