# Tagged Questions

Questions related to understanding line integrals, vector fields, surface integrals, the theorems of Gauss, Green and Stokes. Some related tags are (multivariable-calculus) and (differential-geometry).

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### Stokes' theorem without the smoothness condition

I think I have proved the following version of Stokes' theorem: Teorem 1: Let $\beta: [0,4] \to \mathbb{R}^2$ the curve given by \beta(t) = \begin{cases} (t,0) & \mbox{if } t\...
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### Find for which $\alpha$ $y=8x+\alpha$ is tangent to the curve $x^4+y^4=1$

Find for which $\alpha \in \mathbb{R}$, the line $y=8x+\alpha$ is tangent to the curve $x^4+y^4=1$. Firstly, I calculated the tangent to the curve, which is $(4x^3, 4y^3)$, and if the line is tangent ...
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### Proving the invariance of the mixed product under direct congruent transformations

Text: Differential Geometry, by Erwin Kreyszig Given a set of vectors: $$\overrightarrow{a}=\langle a_1, a_2, a_3 \rangle$$ $$\overrightarrow{b}=\langle b_1, b_2, b_3 \rangle$$  \overrightarrow{...
I know the definition of collinear vectors and the condition for collinearity says "Two vectors $a$ and $b$ are collinear if $a=kb$, $k$ being non-zero scalar" but I am confused if $k=0$ then will not ...