Question

Consider the following vector function.

r(t) = <9t,1/2(t)^{2},t^{2}>

(a) Find the unit tangent and unit normal vectors
**T**(*t*) and
**N**(*t*).

(b) Use this formula to find the curvature.

κ(*t*) =

Answer #1

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) =

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

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...

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 .

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

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) at
the point with the given value of the parameter t.
r(t) =
t2 − 4t, 1 + 5t,
1
3
t3 +
1
2
t2
, t = 5

Consider the following vector function.
r(t) = (3sqrt(2)t, e3t, e−3t )
Find the Curvature.

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

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