Using 3 Vectors to Show Vector Multiplication is Not Commutative

Click For Summary

Homework Help Overview

The discussion revolves around demonstrating that the vector multiplication operation is not commutative using three specific vectors in 3-dimensional space. Participants are tasked with showing that the expression involving the cross product of these vectors does not yield the same result when the order of multiplication is changed.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to compute the cross products of the vectors in different orders and question the clarity of the original poster's attempts. There are requests for detailed steps in the calculations of the cross products.

Discussion Status

Some participants have provided guidance on how to approach the calculations, emphasizing the importance of verifying the properties of the resulting vectors, such as their perpendicularity. There is an acknowledgment of confusion regarding the methods used by the original poster, and further clarification is sought.

Contextual Notes

Participants reference external resources, including PDF files containing solutions, which may not be fully accessible to everyone in the discussion. There is an indication that the original poster may have made assumptions or errors in their calculations that need to be addressed.

amy098yay
Messages
23
Reaction score
0

Homework Statement


That is, use three specific vectors in 3-space to show that https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-a.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117×(https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-b.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117 × https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-c.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117) is not equal to (https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-a.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117 × https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-b.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117) × https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-c.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117.

The Attempt at a Solution


the solution is in the pdf file, did i make a mistake in answering the question..?
 

Attachments

Physics news on Phys.org
..
 
amy098yay said:

Homework Statement


That is, use three specific vectors in 3-space to show that https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-a.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117×(https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-b.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117 × https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-c.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117) is not equal to (https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-a.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117 × https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-b.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117) × https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-c.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117.

The Attempt at a Solution


the solution is in the pdf file, did i make a mistake in answering the question..?
It's hard to follow your work, so I didn't check it. For the first triple product, please show us how you did b X c, and then a X (b X c). For the second triple product, please show is a X b, and then (a X b) X c.

As a self-check for your work, you should verify that when you calculate a X b, for example, the vector you get is perpendicular to both a and b. This can be done very quickly using the dot product - the dot product of perpendicular vectors is 0.
 
another pdf file of the solution
 

Attachments

amy098yay said:
another pdf file of the solution

axb and bxc are ok. I have no idea what you are doing when you try to find (axb)xc and ax(bxc).
 
This is the same sort of problem you're having in the other thread, https://www.physicsforums.com/threads/vectors-need-help.800394/.
 

Similar threads

What is the cross product of two vectors whose result is the zero vector?
  • · Replies 7 ·
Replies
7
Views
2K
Prove RS is parallel to KL using vector method
  • · Replies 20 ·
Replies
20
Views
3K
Working out ##\big[\varphi (x) , \varphi (0) \big]## commutator
  • · Replies 7 ·
Replies
7
Views
2K
Is the Commutator of a Cross Product a Vector Operator?
  • · Replies 4 ·
Replies
4
Views
7K
Showing that Something is a Subspace of R^3
  • · Replies 6 ·
Replies
6
Views
2K
Challenge Intermediate Math Challenge - September 2018
  • · Replies 28 ·
Replies
28
Views
7K
Mathematica How to type mathematical equations using LaTeX
  • · Replies 3 ·
Replies
3
Views
2K
Studying Skipping Chapters in Stewart’s Calculus? (Pearson's Edexcel IAL Background)
  • · Replies 2 ·
Replies
2
Views
1K
Requesting suggestions for languages, libraries, and architectures for parallel (and sometimes non parallel) numerical and scientific computations
  • · Replies 8 ·
Replies
8
Views
4K
Challenge Math Challenge - November 2018
  • · Replies 175 ·
6
Replies
175
Views
27K