Suppose the equations of motion of a particle are x = t − 1 , y = 4 e − t , z = 2 − t , where x = t − 1 , y = 4 e − t , z = 2 − t , where t > 0. Find, to the nearest tenth of a degree, the acute angle between the velocity vector and the normal line to the surface x 2 / 4 + y 2 + z 2 = 1 at the points where the particle collides with the surface. Use a calculating utility with a root-finding capability where needed.
Suppose the equations of motion of a particle are x = t − 1 , y = 4 e − t , z = 2 − t , where x = t − 1 , y = 4 e − t , z = 2 − t , where t > 0. Find, to the nearest tenth of a degree, the acute angle between the velocity vector and the normal line to the surface x 2 / 4 + y 2 + z 2 = 1 at the points where the particle collides with the surface. Use a calculating utility with a root-finding capability where needed.
Suppose the equations of motion of a particle are
x
=
t
−
1
,
y
=
4
e
−
t
,
z
=
2
−
t
,
where
x
=
t
−
1
,
y
=
4
e
−
t
,
z
=
2
−
t
,
where
t
>
0.
Find, to the nearest tenth of a degree, the acute angle between the velocity vector and the normal line to the surface
x
2
/
4
+
y
2
+
z
2
=
1
at the points where the particle collides with the surface. Use a calculating utility with a root-finding capability where needed.
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.
University Calculus: Early Transcendentals (4th Edition)
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