Using 3 Vectors to Show Vector Multiplication is Not Commutative

In summary: You're not doing the problems systematically, so I can't make any real sense of what you're doing, and the problems are simple enough that it's hard for me to tell what you're trying to do. I suggest you go back to the definition of the vector product and work through the examples there carefully.
  • #1
amy098yay
23
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

  • vectors.pdf
    954.3 KB · Views: 270
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  • #2
..
 
  • #3
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.
 
  • #4
another pdf file of the solution
 

Attachments

  • vectorss.pdf
    1 MB · Views: 190
  • #5
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).
 
  • #6
This is the same sort of problem you're having in the other thread, https://www.physicsforums.com/threads/vectors-need-help.800394/.
 

1. What is vector multiplication?

Vector multiplication is a mathematical operation that combines two or more vectors to create a new vector. It is used to represent the relationship between different physical quantities, such as force and velocity.

2. Why is it important to show that vector multiplication is not commutative?

It is important to show that vector multiplication is not commutative because it helps us understand the fundamental properties of vectors and how they interact with each other. It also allows us to make accurate calculations and predictions in various scientific fields, such as physics and engineering.

3. How do you use three vectors to show that vector multiplication is not commutative?

To show that vector multiplication is not commutative, we can use the cross product, which is a type of vector multiplication that results in a vector perpendicular to the original two vectors. By using three vectors and performing cross products in different orders, we can demonstrate that the resulting vectors are not equal, thus proving that vector multiplication is not commutative.

4. What are the implications of vector multiplication not being commutative?

The implications of vector multiplication not being commutative are significant in various scientific disciplines. For example, in physics, it means that the direction of a force can affect the resulting acceleration of an object. In engineering, it means that the order in which forces are applied to a structure can impact its stability and structural integrity.

5. Can you provide a real-life example of vector multiplication not being commutative?

Yes, a real-life example of vector multiplication not being commutative is the calculation of torque. Torque is a vector quantity that represents the rotational force applied to an object. The magnitude and direction of the torque depend on both the magnitude and direction of the force applied and the distance from the axis of rotation. If the force is applied at a different angle, the resulting torque will be different, demonstrating that vector multiplication is not commutative.

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