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

[coconut62]

Please see the image attached.

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

 

[Millennial]

ca = ac, so yes.

 

[coolul007]

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

 

[mark.watson]

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.

 

[mark.watson]

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.

 

[coconut62]

Thank you very much.