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 2 years ago
Referring to vectors, determinants, and cross product: as I understand it the determinant of two 2dimentional vectors yields area, and the determinant of three 3dimentional vectors gives volume. We used determinants to solve volume/area in the coursework.
So, why are we using crossproduct to find volume? Is it simply another method to find the same value?
Thank you
 2 years ago
Referring to vectors, determinants, and cross product: as I understand it the determinant of two 2dimentional vectors yields area, and the determinant of three 3dimentional vectors gives volume. We used determinants to solve volume/area in the coursework. So, why are we using crossproduct to find volume? Is it simply another method to find the same value? Thank you

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hellow
 2 years ago
Best ResponseYou've already chosen the best response.0Correct me if I am wrong. It looks like the magnitude of a cross product actually gives area. So, wouldn't you be using cross products to find area? I think you are right, determinants of a 2x2 also give area of a parallelogram. So, they will probably be easier to use if your vectors are in 2space. But what if your vectors lie in 3space? In that case it may be easier to use the crossproduct for area calculation. (So crossproducts are more general in their application to area calculation. You could use them to find area when your vectors are in 2space or 3space.)
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