Use Stokes’s Theorem to evaluate ∮ C F . d r . F( x , y , z ) = x y i + x 2 j+ z 2 k; C is the intersection of the paraboloid z = x 2 + y 2 and the plane z = y with a counterclockwise orientation looking down the positive z - axis.
Use Stokes’s Theorem to evaluate ∮ C F . d r . F( x , y , z ) = x y i + x 2 j+ z 2 k; C is the intersection of the paraboloid z = x 2 + y 2 and the plane z = y with a counterclockwise orientation looking down the positive z - axis.
F(
x
,
y
,
z
)
=
x
y
i
+
x
2
j+
z
2
k;
C
is the intersection of the paraboloid
z
=
x
2
+
y
2
and
the plane
z
=
y
with a counterclockwise orientation looking down the positive z-axis.
Find the distance from the point (1,1,1) to the plane 2x+2y+z=0
Find an equation of the plane through the three points given:
Р - (0,5, 0),Q — (2, 1, —4), R — (-1,1, —3)
P
= 50
Let L. be the line passing through the point P=(4, -3, 1) with direction vector -[-4, 1, 1], and let T be the plane defined by 5x+4y-4z=37. Find the point Q where L and T intersect.
Q=(0.0.0)
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