Consider the helix represented investigation by the vector-valued function r(t)= &lt; 2 cos⁡ t, 2 sin⁡ t, t &gt;. Solve for t in the relationship derived in part (a), and substitute the result into the original set of parametric equations. This yields a parametrization of the curve in terms of the arc length parameter s.

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Consider the helix represented investigation by the vector-valued function r(t)= &amp;lt; 2 cos⁡ t, 2 sin⁡ t, t &amp;gt;. Solve for t in the relationship derived in part (a), and substitute the result into the original set of parametric equations. This yields a parametrization of the curve in terms of the arc length parameter s.

Brittany Patton · Accepted Answer

The curve in terms of arc legth is r(s)=2 cos⁡ (s5)i + 2 sin⁡ (s5)j + s5k. Given: The function r(t)= &amp;lt; 2 cos⁡ t, 2 sin⁡ t, t &amp;gt; s=(5t) Calculate: The given vector-function for the path is r(t)= &amp;lt; 2 cos⁡ t, 2 sin⁡ t, t &amp;gt;........(1) The length of the curve is  s=(5t)  t= s5t Substituting this value of t in equation (1), we get r(s)= ⟨2 cos⁡ (s5t), 2 sin⁡ (s5t), s5t⟩ Or r(s)=2 cos⁡ (s5)i + 2 sin⁡ (s5)j + s5k. Thus, the curve in terms of arc length is  r(s)=2 cos⁡ (s5)i + 2 sin⁡ (s5)j + s5k.

Consider the helix represented investigation by the vector-valued function r(t)= < 2 cos t, 2 sin t, t >. Solve for t in the relationship derived in p

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