Consider the surface
S
S in
R
3
R
3
which is the graph
z
=
f
(
x
,
y
)
z=f(x,y) of the function
f
(
x
,
y
)
=
x
2
y
cos
(
2
x
y
)
f(x,y)=x
2
ycos(2xy).
Find a parametric description of the line
ℓ
ℓ that intersects
S
S perpendicularly at the point
P
=
(
3
,
1
2
π
,
f
(
3
,
1
2
π
)
)
=
(
3
,
1
2
π
,
−
9
π
2
)
P=(3,
2
1
π,f(3,
2
1
π))=(3,
2
1
π,−
2
9π
).
Use
t
t as a parameter, and give your answer in the form
(
.
.
.
.
.
.
.
.
.
)
+
t
(
.
.
.
.
.
.
.
.
.
)
...
...
...
+t
...
...
...
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