Question

15. Find the principle unit normal vector to the curve given below at the specified point.

r(t)= t i + 4/t j, t=2

Answer #1

Find the unit tangent vector T and the principle unit normal
vector N of ⃗r(t) = cos t⃗i + sin t⃗j + ln(cos t)⃗k at t = π .

20. Find the unit tangent vector T(t) and then use it to find a
set of parametric equations for the line tangent to the space curve
given below at the given point.
r(t)= -5t i+ 2t^2 j+3tk, t=5

At a given point on a smooth space curve r(t), T(t) is the unit
tangent vector, N(t) is the principle unit normal vector and B(t)
is the binormal vector. Which of the following are correct? (The
multiple-choice question might have more than one correct answer.
Circle all correct answers for full credit.) Group of answer
choices
A)None of the above has to be true.
B) T ( t ) ⋅ T ′ ( t ) = 0
C) | B...

Find the unit tangent vector T and the principal unit normal
vector N for the following curve.
r(t) = (9t,9ln(cost)) for -(pi/2) < t < pi/2

Find a unit tangent vector to the curve r = 3 cos 3t
i + 3 sin 2t j at t =
π/6 .

Find the slope of the tangent line to the given polar curve at
the point specified by the value of θ.
r = 4 sin(θ), θ = π/6

Given r(t)=sin(t)i+cos(t)j−ln(cos(t))k, find the unit normal
vector N(t) evaluated at t=0,N(0).

Find the slope of the tangent line to the given polar curve at
the point specified by the value of θ.
r = 5 +
4 cos(θ), θ =
π/3

Find the slope of the tangent line to the given polar curve at
the point specified by the value of θ.
r = 3 + 4 cos(θ), θ = π/3

Find the slope of the tangent line to the given polar curve at
the point specified by the value of θ.
r = 9 + 4 cos(θ), θ = π/3

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