Can area of a triangle be 0.5(c x a) instead of 0.5(a x c)?

Does that have anything to do with directions? The right-hand rule?

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$ca = ac$, so yes.

coolul007
Gold Member
Not in that figure, unless angle B is 90 degrees.

using the magnitude of the cross-product of two vectors to find the ar

If you mean

Area of triangle = (1/2)||A x C|| = (1/2)||C x A||

as in, using the magnitude of the cross-product of two vectors to find the area of the triangle between them, then yes.

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If you mean

Area of triangle = (1/2)||A x C|| = (1/2)||C x A||

as in, using the magnitude of the cross-product of two vectors to find the area of the triangle between them, then yes.
I didn't see the second part of your question. The direction of ||A x C|| or ||C x A|| doesn't matter because they have the same magnitude. That is why (1/2)||A x C|| = (1/2)||C x A|| is true.

Thank you very much.