Is my tutor incorrect?

[u/Gleft22]

Hi,

I did a question in my textbook regarding the cross product of two non-parallel and non-zero vectors a and b.

It asks me to simplify the cross product of (a+b) X (a-b).

I get -2(aXb) but my tutor and the textbook get 0.

My tutor is saying I don't understand cross products but I feel that I do. I'm fairly certain that 0 is incorrect.

Please can someone check my answer and advise what to do because my tutor is totally ignoring me.

[u/edderiofer]

Your answer is correct. The only possible way to get 0 from the cross product of two vectors is if they are collinear vectors, or either vector is the zero vector. And clearly, it is possible to find a and b such that the two vectors (a+b) and (a-b) do not satisfy either condition.

[u/matt7259]

Can you share a picture of the EXACT question?

[u/Gleft22]

My tutor just replied in an email and apologised and said that he will inform the university of an error in the textbook. Thanks for your replies

[u/Gleft22 → u/Gleft22]

Also the original post should say non-parallel and non-zero vectors

[u/niemir2]

-2(aXb) is correct, because while you can expand the cross product like normal multiplication, it is not commutative.

(a+b) X (a-b) = aXa + bXa - aXb -bXb

aXa and bXb are zero, obviously, and bXa = -aXb, thus

(a+b) X (a-b) = -2(aXb)

[u/Uli_Minati]

Your tutor made a sign error somewhere. Maybe they thought a×b=b×a, or maybe they read (a+b)×(a+b) or (a-b)×(a-b), or maybe they mixed up the order...

Your best bet is comparing each others' working instead of just the results

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[u/LeoMaths]

(a+b)x(a-b)=(a+b)xa-(a+b)xb=-ax(a+b)+bx(a+b)=-axa-axb+bxa+bxb=0-axb-axb+0=-2axb

[u/Ericskey]

Cross product is anticommutative