= Constant tangent component forces perpendicular principal normals
{title2=$T\cdot a=\text{constant}\ \Longrightarrow\ N\cdot a=0$}
For a regular <curve> with positive <curvature of a space curve>, the <Frenet-Serret formulas> give $dT/ds=\kappa N$. If the <unit tangent vector> has constant component along a fixed <vector> $a$, differentiation of $T\cdot a$ gives $\kappa N\cdot a=0$. Hence every <principal normal vector> is perpendicular to that direction. Nonzero curvature is needed to define the principal normal.
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