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-Torsion = 0 => B=v, which is a constant

-(α⋅v)'=(T⋅v)'= 0 => α⋅v= a, which is a constant (where α is a function describing the path and T is the tangent vector)

-If α⋅v = constant, then the curve is planar.

Everything up to the end made sense, but I wasn't sure why the professor said that α⋅v= constant is the equation of the plane when the velocity was constant. Can you help me fill in the gaps?