# Help with clifford algebra vector identity

1. Jan 2, 2014

### JBrandonS

1. The problem statement, all variables and given/known data
This is question 1.1 from section 2-1 of New Foundations of Classical Mechanics:

Establish the following "vector identities":
$(a\wedge b) \cdot (c \wedge d) = b\cdot ca \cdot d - b\cdot da \cdot c = b\cdot(c\wedge d)\cdot a$

2. Relevant equations

3. The attempt at a solution
My attempts at this solution make me beleive that there is a typo in this problem. The quickest way is by using the third equation:

$b\cdot(c\wedge d)\cdot a = b \cdot \frac{1}{2}(cd-dc)\cdot a = \frac{1}{2}(b\cdot cd \cdot a - b \cdot dc \cdot a)$

This is equal to half the second equation since $a \cdot b = b \cdot a$. So am I doing something wrong?

2. Mar 28, 2014

### brombo

GA BAC CAB Relations

The generalized BAC CAB relations are shown in the attached file. All the relations were generation using software for the symbolic manipulation of multivectors to be found at

https://github.com/brombo/GA [Broken]

This repository also contains notes on geometric algebra based on Doran and Lasenby. The symbolic software (python modules using sympy) is described in great detail in the "LaTeX docs" directory. It is really easy to make mistakes when doing multivector manipulations by hand.

#### Attached Files:

• ###### BAC_CAB.pdf
File size:
139.5 KB
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37
Last edited by a moderator: May 6, 2017