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

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The area of a triangle can be expressed as 0.5 times the magnitude of the cross-product of two vectors, represented as (1/2)||A x C|| or (1/2)||C x A||. The direction of the vectors does not affect the area calculation since both expressions yield the same magnitude. This relationship holds true regardless of the angle between the vectors, provided angle B is not specifically 90 degrees. The discussion clarifies that the right-hand rule and vector directions are not relevant to the area calculation itself. Overall, the area formula remains consistent across different vector arrangements.
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Please see the image attached.

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

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ca = ac, so yes.
 
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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mark.watson said:
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.
 

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