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Mathematics
Mathematics
Problem
For
r
(
t
)
=
⟨
2
cos
t
,
2
sin
t
,
3
t
⟩
\mathbf r(t)=\langle 2\cos t,\,2\sin t,\,3t\rangle
r
(
t
)
=
⟨
2
cos
t
,
2
sin
t
,
3
t
⟩
, which of the following is true about its curvature
κ
(
t
)
\kappa(t)
κ
(
t
)
? a)
κ
(
t
)
=
1
2
\kappa(t)=\dfrac{1}{2}
κ
(
t
)
=
2
1
for all
t
t
t
. b)
κ
(
t
)
=
2
13
\kappa(t)=\dfrac{2}{\sqrt{13}}
κ
(
t
)
=
13
2
for all
t
t
t
. c)
κ
(
t
)
=
2
13
\kappa(t)=\dfrac{2}{13}
κ
(
t
)
=
13
2
for all
t
t
t
. d)
κ
(
t
)
=
2
13
cos
t
\kappa(t)=\dfrac{2}{13}\cos t
κ
(
t
)
=
13
2
cos
t
.
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