Question

Given r(t)=e^{t}i+e^{-t}j+tk, find the binormal
vector B(0).

Answer #1

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)=

Consider the curve r(t) = i + tj + e^(t)k
a) find the curvature k
b) Find the normal plane at the curve (1,0,1)

Let C be a closed curve parametrized by r(t) = sin ti+cos tj
with 0 ≤ t ≤ 2π. Let F = yi − xj be a vector field.
(a) Evaluate the line integral xyds. C
(b) Find the circulation of F over C. (c) Find the flux of F
over C.

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...

Use the helix: r(t)= (bcost)i +(bsint)j +(ct)k , b>0
I only need e and f. I posted another question where only a-d
were answered if you want to use that work to answer e and f. thank
you
a. find the unit tangent vector
b. find the principal normal vector
c.find the curvature
d.find the binormal vector
e. Find the tangential component of acceleration.
f. find the normal component of acceleration using both
formulas, try to verify that they are...

Recall the Mean Value Theorem: If f : [a, b] → R is continuous
on [a, b], and differentiable on (a, b), then there exists c ∈ (a,
b) such that f(b) − f(a) = f 0 (c)(b − a). Show that this is
generally not true for vector-valued functions by showing that for
r(t) = costi + sin tj + tk, there is no c ∈ (0, 2π) such that r(2π)
− r(0) = 2πr 0 (c).

Find the velocity, acceleration, and speed of a particle with
the given position function.
(a) r(t) = e^t cos(t)i+e^t
sin(t)j+ te^tk, t = 0
(b) r(t) = 〈t^5 ,sin(t)+ t ^ cos(t),cos(t)+ t^2 sin(t)〉, t =
1

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).

Given the vector function r(t) ( cos3t,sin3t,t) and t=pi/9 ,
find the following.
(a) the curvature at given t,
(b) the unit tangent vector T at given t

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

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