Chapter 2: Space Curves
Section 2.3: Tangent Vectors
If Rp is the position vector for the general parametric curve whose components are xp,yp,zp, and s≥0 is arc length, show that ddsRps is necessarily the unit (tangent) vector T.
Recall that dsdp=dxdp2+dydp2+dzdp2, and that dpds=1/dsdp.
Apply the chain rule of differentiation to obtain
Compute the norm, obtaining
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