Find the vector
r
'
t
0
;
then sketch the graph of
r
t
in 2-space and draw the tangent vector
r
'
t
0
.
r
t
=
2
sin
t
i
+
3
cos
t
j
;
t
0
=
π
/
6
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.
Let r(t)=(10 cos(t), 1, 10 sin(t)). Find the unit tangent vector u drawn to point P-(6,1,8).
Sketch curve and tangent.
Let r(t)
(15, cos t, -3 sin t) be the position vector of an object. Find the velocity
and speed of the object.
Find the set of parametric equations for the tangent line to the graph of the vector-valued function
R(t) = (t + sin 3t ,t + cos 3t, In(t + 1)) at the point where t = .
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