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Mathematics
Mathematics
Problem
For the space curve
r
(
t
)
=
⟨
cos
t
,
sin
t
,
t
⟩
\mathbf r(t)=\langle\cos t,\sin t,t\rangle
r
(
t
)
=
⟨
cos
t
,
sin
t
,
t
⟩
, determine the equation of the normal plane at the point corresponding to
t
=
π
/
4
t=\pi/4
t
=
π
/4
. a)
2
x
−
2
y
+
2
z
=
π
2
\sqrt{2}\,x-\sqrt{2}\,y+2z=\dfrac{\pi}{2}
2
x
−
2
y
+
2
z
=
2
π
b)
−
2
x
+
2
y
+
2
z
=
π
2
-\sqrt{2}\,x+\sqrt{2}\,y+2z=\dfrac{\pi}{2}
−
2
x
+
2
y
+
2
z
=
2
π
c)
−
2
x
+
2
y
+
z
=
π
4
-\sqrt{2}\,x+\sqrt{2}\,y+z=\dfrac{\pi}{4}
−
2
x
+
2
y
+
z
=
4
π
d)
−
2
x
+
2
y
+
2
z
=
π
4
-\sqrt{2}\,x+\sqrt{2}\,y+2z=\dfrac{\pi}{4}
−
2
x
+
2
y
+
2
z
=
4
π
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