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r(t)=e^t sin t + e^t cos t + 3

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Laite
Laite 2023-4-26
回答： Aditya Srikar 2023-4-28
Find the unit Tangent vectors, unit Norm vector and binomial vector of the following vector functions. r(t)=e^t sin t + e^t cos t + 3

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Aditya Srikar
Aditya Srikar 2023-4-28
Consider the given vector r(t)
Let r′(t) = d[r(t)] / dt
Let x(t) = r′(t)
The unit tangent vector will be
T(t) = x(t) / |x(t)|
Where |x(t)| represents magnitude of vector x(t).
Let y(t) = T′(t)
The unit normal vector will be
N(t) = y(t) / |y(t)|
Where |y(t)| represents magnitude of vector y(t).
Binormal vector is the cross product of unit tangent and unit normal vectors.
B(t) = T(t) × N(t)
Hope it helps !

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