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## Main Question or Discussion Point

Hey JO,

I'm reading a book on geometric algebra and in the beginning (there was light, jk) a simple calculation is shown:

Geometric product is defined as:

[itex]ab = a \cdot b + a \wedge b[/itex]

or

[itex]ba = a \cdot b - a\wedge b[/itex]

Now

[itex](a\wedge b)(a \wedge b)=(ab-a \cdot b)(a\cdot b - ba)[/itex]

[itex]=-ab^{2}a-(a \cdot b)^{2}+a \cdot b(ab+ba)[/itex]

[itex]=(a \cdot b)^{2}-a^{2}b^{2}[/itex]

[itex]=-a^{2}b^{2}sin^{2}(\phi)[/itex]

I think this term [itex]a \cdot b(ab+ba)[/itex] has to vanish somehow, but it is [itex]

(a\cdot b)^{2}[/itex] and that doesn't make sense :( Any suggestions?

Ok I know the answer, the term is [itex]2(a\cdot b)^{2}[/itex]. But thank you for your attention !

I'm reading a book on geometric algebra and in the beginning (there was light, jk) a simple calculation is shown:

Geometric product is defined as:

[itex]ab = a \cdot b + a \wedge b[/itex]

or

[itex]ba = a \cdot b - a\wedge b[/itex]

Now

[itex](a\wedge b)(a \wedge b)=(ab-a \cdot b)(a\cdot b - ba)[/itex]

[itex]=-ab^{2}a-(a \cdot b)^{2}+a \cdot b(ab+ba)[/itex]

[itex]=(a \cdot b)^{2}-a^{2}b^{2}[/itex]

[itex]=-a^{2}b^{2}sin^{2}(\phi)[/itex]

I think this term [itex]a \cdot b(ab+ba)[/itex] has to vanish somehow, but it is [itex]

(a\cdot b)^{2}[/itex] and that doesn't make sense :( Any suggestions?

Ok I know the answer, the term is [itex]2(a\cdot b)^{2}[/itex]. But thank you for your attention !

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