Question

Find T, N, and B for the given space curve.

r(t) = (t^{2}-9)i + (2t-9)j + 4k

Answer #1

6. Given vector function r(t) = t2 − 2t, 1 + 3t, 1 3 t 3 + 1 2 t
2 i (a) Find r 0 (t) (b) Find the unit tangent vector to the space
curve of r(t) at t = 3. (c) Find the vector equation of the tangent
line to the curve at t = 3

Find T, N, B, aT, aN at t=2 (#13)
13. r(t) = (t3/3)i + (t2/2)j when t >
0

Let C be the curve parametrized by r(t)=(t2+2)i+(1+t)j+2t^2k,
with 0≤t≤. Consider the conservative vector field
F=yz2i+xz2j+2xyzk, Calculate ∫CF⋅dr

Find the speed of the particle with position function
r(t) = (t2 − 2t)⃗i − 2t⃗j + (t2 − t)⃗k when t = 0.

Consider the curve r(t) = cost(t)i + sin(t)j +
(2/3)t2/3k
Find:
a. the length of the curve from t = 0 to t = 2pi.
b. the equation of the tangent line at the point t = 0.
c. the speed of the point moving along the curve at the point t
= 2pi

Let C be the plane curve determined by the function
r(t)=(3-t^2)i+(2t)j where -2<=t<=2.
-Find T(t), T'(t), the magnitude of T'(t), and
N(t).
Please show work, Thank you!

18. Find aT at time t=2 for the space curve r(t)= (9t-1)i + t^2
j -8tk

Find the curvatures of the given curves.
i: r(t) = ⟨t, t2/2, t2⟩
ii: r(t) = ti + t2j + etk

Find the vectors T and N and
the binormal vector B = T ⨯
N, for the vector-valued function
r(t) at the given value of
t.
r(t) = 6 cos(2t)i + 6
sin(2t)j +
tk, t0 =
pi/4
find:
T(pi/4)=
N(pi/4)=
B(pi/4)=

Find the curvature of ~r(t) = (t3 −5)~ i + (t4 + 2)~ j + (2t +
3)~ k at the point P(−6,3,1)?

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