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 formed by two vectors A and C can be calculated using the formula Area = 0.5 * ||A x C||, which is equivalent to Area = 0.5 * ||C x A||. The direction of the cross-product does not affect the area calculation, as both expressions yield the same magnitude. This relationship holds true regardless of the angle between the vectors, provided that they are not collinear.

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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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