French Osborne
02/02/2024 · High School
Consider the helix \( \mathbf{r}(t)=\langle\cos (8 t), \sin (8 t), 1 t\rangle \). Compute, at \( t=\frac{\pi}{6} \) : A. The unit tangent vector \( \mathbf{T}=\langle \) B. The unit normal vector \( \mathbf{N}=\langle \) C. The unit binormal vector \( \mathbf{B}=\langle \) Submit answer
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A. The unit tangent vector \( \mathbf{T} = \left\langle \frac{4\sqrt{3}}{\sqrt{65}}, \frac{-4}{\sqrt{65}}, \frac{1}{\sqrt{65}} \right\rangle \)
B. The unit normal vector \( \mathbf{N} = \left\langle \frac{1}{2}, \frac{\sqrt{3}}{2}, 0 \right\rangle \)
C. The unit binormal vector \( \mathbf{B} = \left\langle -\frac{\sqrt{3}}{2\sqrt{65}}, \frac{1}{2\sqrt{65}}, \frac{3}{\sqrt{65}} \right\rangle \)
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