Eliminate the parameter t, write the equation in Cartesian coordinates, then sketch the graphs of the vector -valued functions. 25. r ( t ) = 3 ( cos t ) i + 3 ( sin t ) j
Eliminate the parameter t, write the equation in Cartesian coordinates, then sketch the graphs of the vector -valued functions. 25. r ( t ) = 3 ( cos t ) i + 3 ( sin t ) j
Eliminate the parameter t, write the equation in Cartesian coordinates, then sketch the graphs of the vector-valued functions.
25.
r
(
t
)
=
3
(
cos
t
)
i
+
3
(
sin
t
)
j
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.
The equation r(t) = (3 sin t) i + (3 cos t)j + (t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at
t=2x as a product of its speed and direction.
The velocity vector is v(t)=i+j+ k.
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