Trajectories on circles and spheres Determine whether the following trajectories lie on a circle in ℝ 2 or sphere in ℝ 3 centered at the origin. If so, find the radius of the circle or sphere and show that the position vector and the velocity vector are everywhere orthogonal. 30. r ( t ) = 〈 3 cos t + 2 sin t , − 3 cos t + 2 sin t , 2 sin t 〉 , for 0 ≤ t ≤ 2 π
Trajectories on circles and spheres Determine whether the following trajectories lie on a circle in ℝ 2 or sphere in ℝ 3 centered at the origin. If so, find the radius of the circle or sphere and show that the position vector and the velocity vector are everywhere orthogonal. 30. r ( t ) = 〈 3 cos t + 2 sin t , − 3 cos t + 2 sin t , 2 sin t 〉 , for 0 ≤ t ≤ 2 π
Solution Summary: The author determines whether the given trajectory lies on a circle or sphere in R3 centered at origin. The position vector and velocity vector are everywhere orthogonal.
Trajectories on circles and spheresDetermine whether the following trajectories lie on a circle in
ℝ
2
or sphere in
ℝ
3
centered at the origin. If so, find the radius of the circle or sphere and show that the position vector and the velocity vector are everywhere orthogonal.
30.
r
(
t
)
=
〈
3
cos
t
+
2
sin
t
,
−
3
cos
t
+
2
sin
t
,
2
sin
t
〉
, for 0 ≤ t ≤ 2π
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.
=
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0
Ne
Na
Ny
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No.of blows, N 11 15 29 32 30 44
0
estigate shear
12%
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