Simplify a Dot/Corss product

Nov 2009
58
0
Hi,

I have a question - Simplify 'a X (b + c) . b'

which has an answer of 'a X c . b'

How have they come to that?

The only thing I see is perhaps taking it to (a X b) + (a X c) . b but doesn't really help .

Thanks
 

Opalg

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Aug 2007
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Leeds, UK
Hi,

I have a question - Simplify 'a X (b + c) . b'

which has an answer of 'a X c . b'

How have they come to that?

The only thing I see is perhaps taking it to \(\displaystyle \color{red}\big(\)(a X b) + (a X c)\(\displaystyle \color{red}\big)\) . b but doesn't really help .
You have started off in the right way, but don't forget those parentheses (in red above). When you multiply them out, you get
(a X b) . b + (a X c) . b . But a X b is orthogonal to b, so (a X b) . b = 0, and you are just left with (a X c) . b .
 
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Nov 2009
58
0
Fantastic, thank you very much.

If i've got my wording correct is the Dot Product 'Distributive across addition'?

Thanks again.