(a) Find the unit tangent and unit normal vectors T ( t ) and N ( t ) . (b) Use Formula 9 to find the curvature. 19. r ( t ) = t 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 ) . (b) Use Formula 9 to find the curvature. 19. r ( t ) = t 2 , sin t − t cos t , cos t + t sin t , t > 0
Solution Summary: The author explains how to find the unit tangent vector and unit normal vector.
(a) Find the unit tangent and unit normal vectors
T
(
t
)
and
N
(
t
)
.
(b) Use Formula 9 to find the curvature.
19.
r
(
t
)
=
t
2
,
sin
t
−
t
cos
t
,
cos
t
+
t
sin
t
,
t
>
0
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.
r(t) = (2cos t)i+ (2sin t)j + (V5 t)k,
Find the curve's unit tangent vector.
T(1) = Di+Dj+D
k
Enter your answer in the edit fields and then click Check Answer.
The motion of a point on the circumference of a rolling wheel of radius 5 feet is described by the vector
function
7(t)
5(13t – sin(13t))ỉ + 5(1 – cos(13t))j
Find the velocity vector of the point.
히(t) =D
Find the acceleration vector of the point.
a(t) =
Find the speed of the point.
s(t) =
Check Answer
Consider the vector function given below.
r(t) =
7t, 5 cos(t), 5 sin(t)
(a)
Find the unit tangent and unit normal vectors T(t) and N(t).
T(t)
=
N(t)
(b)
Use the formula
?(t) =
|T ′(t)|
|r ′(t)|
to find the curvature.
?(t) =
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