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Mathematics
Problem
Find the unit tangent vector
T
(
t
)
\mathbf{T}(t)
T
(
t
)
at the point with the given value of the parameter
t
t
t
.
r
(
t
)
=
⟨
t
2
−
2
t
,
1
+
3
t
,
1
3
t
3
+
1
2
t
2
⟩
,
t
=
2
\mathbf{r}(t) = \langle t^2 - 2t, 1 + 3t, \frac{1}{3}t^3 + \frac{1}{2}t^2 \rangle, t = 2
r
(
t
)
=
⟨
t
2
−
2
t
,
1
+
3
t
,
3
1
t
3
+
2
1
t
2
⟩
,
t
=
2
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