Using 3 Vectors to Show Vector Multiplication is Not Commutative

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The discussion focuses on demonstrating that vector multiplication is not commutative using three specific vectors in 3-space. Participants express confusion over the calculations involved in the triple products a × (b × c) and (a × b) × c. There is a suggestion to verify results by checking that the cross products yield vectors perpendicular to the original vectors, using the dot product for confirmation. Some users indicate difficulty in following the calculations presented and request clearer steps for the vector operations. The conversation emphasizes the importance of correctly applying vector multiplication rules to illustrate the non-commutative property effectively.
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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

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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/.
 

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