Question

Consider the following vector function.

r(t) =

6t^{2}, 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*) =

Answer #1

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 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 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 .

Given r(t) = (et cos(t) )i + (et sin(t) )j
+ 2k. Find
(i) unit tangent vector T.
(ii) principal unit normal vector N.

1. A plane curve has been parametrized with the following
vector-valued function, r(t) = (t + 2)i + (-2t2 + t + 1)j a.
Carefully make 2 sketches of the plane curve over the interval . (5
pts) b. Compute the velocity and acceleration vectors, v(t) and
a(t). (6 pts) c. On the 1st graph, sketch the position, velocity
and acceleration vectors at t=-1. (5 pts) d. Compute the unit
tangent and principal unit normal vectors, T and N at...

Consider the ellipse r(t) =〈3 cos(t),4 sin(t)〉, for 0 ≤ t ≤
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(a) At what positions does ‖r′(t)‖ have maximum and minimum
values, that is, where is a particle moving along the ellipse
moving the fastest and slowest? Your answer will be vectors.
(b) At what positions does the curvature have maximum and
minimum values? Your answer will be vectors.

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

17.)Find the curvature of r(t) at the
point (1, 0, 0).
r(t) =
et
cos(t),
et
sin(t), 3t
κ =

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

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

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