Question

Consider the following vector function.

r(t) = (3sqrt(2)t, e^{3t}, e^{−3t} )

Find the Curvature.

Answer #1

Find the derivative r '(t) of the
vector function r(t).
<t cos 3t , t2, t sin 3t>

Consider the following vector function.
r(t) = <9t,1/2(t)2,t2>
(a) Find the unit tangent and unit normal vectors
T(t) and
N(t).
(b) Use this formula to find the curvature.
κ(t) =

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

Find the unit tangent vector T(t) and the curvature κ(t) for the
curve r(t) = <6t^3 , t, −3t^2 >.

Find the curvature of r(t) at the
point (3, 1, 1).
r(t) = <3t, t^2 , t^3>
k=

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 the curvature of the space curve x=(3t^2)-t^3 y=3t^2
z=(3t)+t^3

Find the curvature, k(t), of the following:
r(t) = t i + t^2
j + e^t k

Consider the following vector function.
r(t) =
6t2, sin(t) − t cos(t), cos(t) + t sin(t)
, t > 0
(a) Find the unit tangent and unit normal vectors
T(t) and
N(t).
T(t)
=
N(t)
=
(b) Use this formula to find the curvature.
κ(t) =

Let r(t) = < 2cost, 3t, 2sint > represent a parameterized
curve. Find the:
a) unit tangent vector
b) unit normal vector
c) curvature

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