#### aceband

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

MHF Hall of Honor
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 .

aceband

#### aceband

Fantastic, thank you very much.

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

Thanks again.

#### Opalg

MHF Hall of Honor
If i've got my wording correct is the Dot Product 'Distributive across addition'?
Yes. (Rock)