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.
Consider the following function.
T: R2 → R, T(x, y) = (2x2, 3xy, y?)
Find the following images for vectors u =
(u,, u2) and v = (v,, v2) in R2 and the scalar c. (Give all answers in terms of
1'
"1, U2, V1, V2, and c.)
T(u)
T(v)
T(u) + T(v) =
T(u + v)
CT(u) =
T(cu) =
Determine whether the function is a linear transformation.
O linear transformation
not a linear transformation
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