just wanted to see 2 proofs if anyone knows them or where I can point my browser to see them please,

just proofs for these cross products where a and b are vectors and c is scalar.

just a x b = -b x a

and

a x (b + c) = a x b + a x c

thankyou.

Printable View

- Feb 23rd 2009, 09:24 PMrcmangoproof of two cross products.
just wanted to see 2 proofs if anyone knows them or where I can point my browser to see them please,

just proofs for these cross products where a and b are vectors and c is scalar.

just a x b = -b x a

and

a x (b + c) = a x b + a x c

thankyou. - Feb 23rd 2009, 10:11 PMo_O
Let and .

Recall that if you have a matrix and you interchange two of its rows to form a matrix , then .

Applying this here:

But this is what we were looking for! How is defined? Is this what we have? Yep.

_____________

For the second one, there is always the tedious route of calculating both sides and showing that they are indeed equal.

Start by letting: and and - Feb 23rd 2009, 10:26 PMrcmango
i found something on wiki, this was more of what I was looking for, but is what you have defined above an easier way to do this than what i have found here?

of course this is just part of the proof, there needs to be factoring further.

Its just alot of work it seems, to prove it correctly.

a × b = (a1i + a2j + a3k) × (b1i + b2j + b3k)

a × b = a1i × (b1i + b2j + b3k) + a2j × (b1i + b2j + b3k) + a3k × (b1i + b2j + b3k)

a × b = (a1i × b1i) + (a1i × b2j) + (a1i × b3k) + (a2j × b1i) + (a2j × b2j) + (a2j × b3k) + (a3k × b1i) + (a3k × b2j) + (a3k × b3k).