Find the flux of the vector field F across σ in the direction of positive orientation. F( x , y , z ) = x 2 + y 2 k; σ is the portion of the cone r ( u , v ) = u cos v i + u sin v j + 2 u k with 0 ≤ u ≤ sin v , 0 ≤ v ≤ π .
Find the flux of the vector field F across σ in the direction of positive orientation. F( x , y , z ) = x 2 + y 2 k; σ is the portion of the cone r ( u , v ) = u cos v i + u sin v j + 2 u k with 0 ≤ u ≤ sin v , 0 ≤ v ≤ π .
Find the flux of the vector field F across
σ
in the direction of positive orientation.
F(
x
,
y
,
z
)
=
x
2
+
y
2
k;
σ
is the portion of the cone
r
(
u
,
v
)
=
u
cos
v
i
+
u
sin
v
j
+
2
u
k
with
0
≤
u
≤
sin
v
,
0
≤
v
≤
π
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Find an equation of the plane tangent to the Bohemian dome S described by the vector function
R(u, v) = (2 cos u, 2 sin u + sin v, cos v)
at the point where u = π/6 and v= π/2.
b) Given the vector field F(x, y, z) = y² tan 2x i - (lnx) (sin z)j + ey k.
Find
i. div F
ii. curl F
iii. V. (V x F)
1) Sketch the vector field F.
(i) F(r
,y) =
(ii) F(r, y, 2) -i
7.
3Di
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
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