Is Addition Distributive Over the Dot Product in Vector Calculations?

  • Thread starter amy098yay
  • Start date
In summary, verifying equations is crucial in science to ensure accuracy and validity of findings. The equation A(B+C) ≠ AB+AC means the distributive property does not apply. There are no exceptions to this equation and it has real-world applications in fields such as economics and engineering. An example of this equation is demonstrated in calculating the area of a rectangular garden.
  • #1
amy098yay
23
0

Homework Statement


Verify using an example that a(b+c) is not equal to ab+ac. (This means that addition does not distribute over the dot product.)

Vector A be in the y direction (Ax=0 , Ay=1 , Az = 0)
Vector B be in the x direction (Bx=1 , By=0 , Bz = 0)

so, Vector A×B components:

x = Ay * Bz - By * Az = 0
y = Az * Bx - Bz * Ax = 0
z = Ax * By - Bx * Ay = -1

so,

AxB = (0 , 0 , -1)

would this work?

Homework Equations

The Attempt at a Solution

 
Physics news on Phys.org
  • #2
Please don't start new threads when you have another thread open on the same problem.
 

FAQ: Is Addition Distributive Over the Dot Product in Vector Calculations?

1. Why is it important to verify the equation A(B+C) ≠ AB+AC in science?

In science, it is important to verify equations in order to ensure the accuracy and validity of our findings. If we do not verify equations, we run the risk of drawing incorrect conclusions and making faulty predictions, which can hinder progress in our understanding of the natural world. By verifying the equation A(B+C) ≠ AB+AC, we can ensure that our mathematical reasoning is sound and that our experimental results are reliable.

2. What does the equation A(B+C) ≠ AB+AC mean?

This equation is stating that the expanded form of A multiplied by the sum of B and C is not equal to the product of A and B added to the product of A and C. In other words, the distributive property does not apply in this scenario.

3. Are there any exceptions to the equation A(B+C) ≠ AB+AC?

No, this equation holds true for all values of A, B, and C. It is a fundamental rule in mathematics and has been proven to be true through various mathematical proofs and experiments.

4. How is the equation A(B+C) ≠ AB+AC relevant in real-world applications?

The equation A(B+C) ≠ AB+AC is relevant in real-world applications as it helps us understand the limitations of the distributive property in certain scenarios. It is commonly used in fields such as economics, physics, and engineering to accurately model and analyze systems and behavior.

5. Can you provide an example to demonstrate the equation A(B+C) ≠ AB+AC?

Sure, let's say we have a rectangular garden with a length of 5 meters and a width of 3 meters. If we want to find the total area of the garden, we could use the equation A = L x W, where A represents the area, L represents the length, and W represents the width. If we use the distributive property and expand the equation to A = (2+3)(2), we get 10 square meters. However, if we try to use the equation A = 2L + 3L, we get 25 square meters, which is not equal to the previous result. Therefore, we can see that A(B+C) ≠ AB+AC in this scenario.

Similar threads

Replies
6
Views
2K
Replies
2
Views
3K
Replies
5
Views
2K
Replies
3
Views
2K
Replies
3
Views
2K
Replies
4
Views
1K
Replies
3
Views
1K
Back
Top