How Is Curvature Calculated Using Vector Functions?

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Curvature can be calculated using vector functions by transforming the formula T'(t) / r'(t) into the expression | r'(t) x r"(t) | / | (r'(t))^3 |. The discussion highlights the need for clarity on the derivation of this formula. Participants are encouraged to share insights and solutions related to this transformation. There is also a suggestion to merge this topic with another related thread for better continuity. Understanding this calculation is essential for solving problems involving curvature in vector calculus.
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Homework Statement



can someone explain how to turn the formula of curvature T'(t) / r'(t) into | r'(t) x r"(t) | / | (r't)^3 | ?

Homework Equations

The Attempt at a Solution


my working is in 317.jpgT'(t) / r'(t) <blockquote class="imgur-embed-pub" lang="en" data-id="a/q3t1U"><a href="//imgur.com/q3t1U"></a></blockquote><script async src="//s.imgur.com/min/embed.js" charset="utf-8"></script>

[PLAIN]http://imgur.com/a/q3t1U[/B]
 

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@chetzread -- Please post this in your other thread. Thank you.
 

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