Menu Close

Prove-that-The-necessary-and-sufficient-condition-that-the-curve-be-plane-curve-is-r-r-r-0-OR-A-curve-is-plane-curve-iff-0-




Question Number 70876 by Fakhar last updated on 09/Oct/19
Prove that  The necessary and sufficient condition  that the curve be plane (curve) is              [r′,r′′,r′′′]=0.   OR      A curve is plane curve iff τ=0.
$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{The}\:\mathrm{necessary}\:\mathrm{and}\:\mathrm{sufficient}\:\mathrm{condition} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{be}\:\mathrm{plane}\:\left(\mathrm{curve}\right)\:\mathrm{is} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{\mathrm{r}}',\boldsymbol{\mathrm{r}}'',\boldsymbol{\mathrm{r}}'''\right]=\mathrm{0}. \\ $$$$\:\mathrm{OR}\:\:\:\: \\ $$$$\mathrm{A}\:\mathrm{curve}\:\mathrm{is}\:\mathrm{plane}\:\mathrm{curve}\:\mathrm{iff}\:\tau=\mathrm{0}. \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *