Find the flux of F x , y , z = x i + y j + 2 z k through the portion of the paraboloid z = 1 − x 2 − y 2 that is on or above the xy -plane, with upward orientation.
Find the flux of F x , y , z = x i + y j + 2 z k through the portion of the paraboloid z = 1 − x 2 − y 2 that is on or above the xy -plane, with upward orientation.
Find the flux of
F
x
,
y
,
z
=
x
i
+
y
j
+
2
z
k
through the portion of the paraboloid
z
=
1
−
x
2
−
y
2
that is on or above the xy-plane, with upward orientation.
Determine the scalar equation of the plane that contains A(-1, 3, 1) and is
perpendicular to both 5x - 2y+z-6=0 and 4x + y 2z+ 9 = 0.
Find
F-dS if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z =
8-a?-y?
lying above the rectangle [0, 1] × [0, 2] and has upward orientation.
285. Find the scalar equation of the plane that passes
through point P(-1, 2, 1) and is perpendicular to the line
of intersection of planes x+y-z-2=0 and
2xy + 3z-1=0.
University Calculus: Early Transcendentals (3rd Edition)
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