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.
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.
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.
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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
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).