Unit Tangent Vector If we let C be a smooth curve with position vector r → ( t), then the Unit Tangent Vector, denoted T → ( t), is defined to be T → ( t) = r → ′ ( t) ‖ r → ′ ( t) ‖
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If we had →r ′(t) = →0 r → ′ ( t) = 0 → we would have a vector that had no magnitude and so couldn’t give us the direction of the tangent. Also, provided →r ′(t) ≠ →0 r → ′
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