Proved A x [B x (Cx D) ] = 0

  • Thread starter SAMIA
  • Start date
In summary, Samia tried to prove this theorem using vectors in R3, but failed. The theorem can't be proven, because it is false, and when she attempted to use vectors that would work the theorem became false.
  • #1
SAMIA
1
0
Hello I hope you can help me in solving this proof

proved A x [B x (Cx D) ] = 0


Thank you
 
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  • #2
Hello Samia, welcome to PF. Since this is your first post you may not have read the rules, one of which is you must show what you have tried. Nevertheless I will give you a Hint: Try the calculation with 4 different vectors.
 
  • #3
LCKurtz said:
Hello Samia, welcome to PF. Since this is your first post you may not have read the rules, one of which is you must show what you have tried. Nevertheless I will give you a Hint: Try the calculation with 4 different vectors.

that's just...cruel.

presumably A,B,C and D lie in R3?

if so, A must be a linear combination of B,C, and D.

the cross-product is distributive, is it not?

from here it get easy...because of a certain elementary property of cross-products.
 
  • #4
Deveno said:
that's just...cruel.

presumably A,B,C and D lie in R3?

if so, A must be a linear combination of B,C, and D.

the cross-product is distributive, is it not?

from here it get easy...because of a certain elementary property of cross-products.

How does it get easy when it is false? And what is cruel about suggesting that most anything will give a counterexample?
 
  • #5
LCKurtz said:
How does it get easy when it is false? And what is cruel about suggesting that most anything will give a counterexample?

except, obviously, for the ones i tried. please excuse me while i shave my facial omelette.
 
  • #6
This theorem can't be proved, because (as noted by LCKurtz) it is simply false. A simple counter can be shown by letting A=B=C=i, D=j where i,j, and k are the unit vectors in the x,y, and z directions (respectively). Then

A x (B x (C x D))=i x (i x (i x j))
=i x (i x (k))
=i x (-j)
A x (B x (C x D))=-k0
 

1. What does the equation "Proved A x [B x (Cx D) ] = 0" represent?

This equation represents a mathematical statement that has been proven to be true, where A, B, C, and D are variables that are multiplied together and equal 0.

2. How is this equation useful in scientific research?

Equations like this are fundamental to many scientific disciplines, as they allow us to describe and understand complex systems and phenomena in a quantitative way. This particular equation may be used to represent a relationship between different variables in a scientific experiment, for example.

3. What does the "x" symbol represent in this equation?

The "x" symbol in this equation represents multiplication, indicating that the variables on either side of the symbol are being multiplied together to form the final result.

4. Is the "0" at the end of the equation significant?

Yes, the "0" at the end of the equation is significant. It indicates that the whole equation equals 0, which is a special case in mathematics and can have important implications in scientific research. It could mean that there is no relationship between the variables or that one variable is dependent on the others.

5. How does one prove an equation like this?

Proving an equation like this involves using mathematical principles and logical reasoning to show that the equation holds true for all possible values of the variables involved. This requires a combination of knowledge, critical thinking, and problem-solving skills.

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