I am studying differential forms and have difficulty with the following question：Suppose $v_1,v_2$ are two vectors in $\mathbb{R}^n$, $S$ is the triangle spanned by $v_1,v_2$ and $S_1$ is the projection of $S$ onto the plane $x_1Ox_2$.Then how to use $v_1,v_2$ to represent the signed area of $S_1$? And this induces a 2-form.
2026-04-13 07:50:40.1776066640
Representations of signed areas
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(Signed) area of $S_1$ $=dx_1\wedge dx_2(v_1,v_2)$