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SSC Pure Mathematics QUESTION #11195
Question 1
With the notation from the previous question, $\tau\mathbf{b} - k\mathbf{t} =$
  • $\dfrac{d\mathbf{t}}{ds}$
  • $\dfrac{d\mathbf{n}}{ds}$✔️
  • $\dfrac{d\mathbf{b}}{ds}$
  • $\dfrac{d}{ds}(\mathbf{t}\times\mathbf{n})$
Correct Answer Explanation
The Frenet-Serret formulae are: $\dfrac{d\mathbf{t}}{ds} = k\mathbf{n}$, $\dfrac{d\mathbf{n}}{ds} = -k\mathbf{t} + \tau\mathbf{b}$, $\dfrac{d\mathbf{b}}{ds} = -\tau\mathbf{n}$, where $k$ is curvature and $\tau$ is torsion. Therefore $\tau\mathbf{b} - k\mathbf{t} = \dfrac{d\mathbf{n}}{ds}$.