Help with physics demonstration

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Homework Help Overview

The discussion revolves around a physics demonstration involving vector operations, specifically the cross product and dot product. The original poster seeks assistance in proving a relationship between vectors based on given equations.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definitions of the dot and cross products, questioning the implications of the equations provided. There is an attempt to clarify the meaning of "a x b" and "a.b" and how they relate to vector multiplication. Some participants express confusion over the original poster's findings and suggest that more information is needed to proceed with the demonstration.

Discussion Status

The discussion is ongoing, with participants actively questioning definitions and exploring the implications of the equations. Some guidance has been offered regarding the need for clarity on vector operations, but no consensus has been reached on how to demonstrate the original poster's claim.

Contextual Notes

There is a lack of clarity regarding the definitions of the dot and cross products, which is impacting the ability to address the original problem effectively. The original poster's hint and subsequent findings have led to confusion among participants.

brad sue
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Hi ,
Please can I have some help with this demonstration:
Let a#0 ( #= different)
Show that if a x b = a x c and a.b=a.c, then b=c ( Hint: Cross both sides of the first equation with a)
When I cross by a ( as the hint suggests) , I found 0=0 ??
thank you
 
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What is "a x b" vs. "a.b"?
 
What are your definitions of The dot and cross product?
 
Integral said:
What are your definitions of The dot and cross product?
Hi , I don't know what you mean but I guess you want to know that
"a x b" means a cross product with b
and
"a.b" mean a dot b
Thank you
B
 
brad sue said:
Hi , I don't know what you mean but I guess you want to know that
"a x b" means a cross product with b
and
"a.b" mean a dot b
Thank you
B
Right. So, is "dot" vector multiplication? How is "cross product" different than vector multiplication? Some examples would be useful. What is (1,2) x (3,4)? What is (1,2).(3,4)?
Let's say a, b, and c are vectors. Let a=(1,2), b=(1,2) and c=(c1,c2).
ab = ac ---> a1b1 + a2b2 = a1c1 + a2c2 ---> 5 = c1 + 2 c2 ---> c1 = 5 - 2 c2, which means that although c = (1,2) would satisfy the equation, so would c = (5,0). Therefore what you want to demonstrate is not demonstrable on the basis of vector multiplication alone. That is why more info is needed on the exact definitions of the cross and the dot.

My guess is they are inner and outer products: a.b = a1b1 + a2b2, axb = (a1b1, a1b2, a2b1, a2b2). But can you verify this so we won't be making a mistake?
 
Last edited:

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