Cross Product of Two Vectors Explained!
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- Опубликовано: 28 апр 2017
- 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...
___________________________________
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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!
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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 RUclips TV with the Organic Chemistry Tutor.
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If you're looking for a good visual demonstration of cross product and the right hand rule check out my explanation at ruclips.net/video/zBe0hz40eT4/видео.html
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"
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.
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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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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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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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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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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