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Hawkingo

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- Thread starter Hawkingo
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- #1

Hawkingo

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- #2

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The direction is determined by the right hand rule: thumb ##\vec{a}##, pointer ##\vec{b}##, middle ##\vec{a}\times \vec{b}##.

- #3

Hawkingo

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I know but I want to ask that why consider ##\vec{a}\times \vec{b}## for the area of the triangle but not ##\vec{b}\times \vec{a}## ? The 2 cross products have different directions.The direction is determined by the right hand rule: thumb ##\vec{a}##, pointer ##\vec{b}##, middle ##\vec{a}\times \vec{b}##.

- #4

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Like with all things which can be oriented: make your choice! Why do we write debts as negative numbers and not the other way around? Why do we define ##\int_a^b f(x)dx = F(b)-F(a)## and not the other way around? It's only a convention, and in this case I find it suited compared with the formula behind: ##(\vec{a}\times \vec{b})_1=+ \det\left(\begin{bmatrix}a_2& b_2\\a_3&b_3\end{bmatrix} \right)##, i.e. to start with a positive sign.I know but I want to ask that why consider ##\vec{a}\times \vec{b}## for the area of the triangle but not ##\vec{b}\times \vec{a}## ? The 2 cross products have different directions.

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