For each surface
r
‾
(
u
,
v
)
\displaystyle \overline{{r}}{\left({u},{v}\right)}
r
(
u
,
v
)
, identify the best description of the surface's shape.
r
‾
(
u
,
v
)
\displaystyle \overline{{r}}{\left({u},{v}\right)}
r
(
u
,
v
)
-
a
b
c
d
<
v
2
,
u
,
v
>
\displaystyle <{v}^{{2}},{u},{v}>
<
v
2
,
u
,
v
>
-
a
b
c
d
<
cos
(
u
)
,
v
,
sin
(
u
)
>
\displaystyle <{\cos{{\left({u}\right)}}},{v},{\sin{{\left({u}\right)}}}>
<
cos
(
u
)
,
v
,
sin
(
u
)
>
-
a
b
c
d
<
v
cos
(
u
)
,
v
2
,
v
sin
(
u
)
>
\displaystyle <{v}{\cos{{\left({u}\right)}}},{v}^{{2}},{v}{\sin{{\left({u}\right)}}}>
<
v
cos
(
u
)
,
v
2
,
v
sin
(
u
)
>
-
a
b
c
d
<
v
cos
(
u
)
,
v
,
v
sin
(
u
)
>
\displaystyle <{v}{\cos{{\left({u}\right)}}},{v},{v}{\sin{{\left({u}\right)}}}>
<
v
cos
(
u
)
,
v
,
v
sin
(
u
)
>
Shape
cone
parabolic cylinder
paraboloid
cylinder
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