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Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) = ti + (8/t) j, t = 2

User SSH
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Final answer:

The principal unit normal vector to the curve at the specified value of the parameter is -2j.

Step-by-step explanation:

To find the principal unit normal vector to the curve at the specified value of the parameter, we need to calculate the second derivative of the position vector r(t) = ti + (8/t)j and evaluate it at t = 2.

The second derivative of r(t) is given by r''(t) = (0i - 8/t^2j) = -8/t^2j.

At t = 2, the principal unit normal vector is n(2) = (-8/2^2)j = -2j.

User Lionel Henry
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