4. [7 points] Find the binormal unit vector for \( \mathbf{r}(t) = (2e^t, e^t \cos(t), e^t \sin(t)) \) at \( t_0 = 0 \)
Added by George F.
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Step 1
First, we need to find the tangent and normal vectors at t=0. The tangent vector is given by the derivative of the position vector with respect to t: r'(t) = (0, -sin(t), 4e^t cos(4t)) At t=0, this becomes r'(0) = (0, 0, 4) So the tangent vector at t=0 is (0, 0, Show moreā¦
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