Find the flux of the vector field F across σ in the direction of positive orientation. Find the flux of the vector field F across σ in the direction of positive orientation. F( x , y , z ) = x i + y j + z k; σ is the portion of the sphere r ( u , v ) = 2 sin u cos v i + 2 sin u sin v j + 2cos u k with 0 ≤ u ≤ π / 3 , 0 ≤ v ≤ 2 π .
Find the flux of the vector field F across σ in the direction of positive orientation. Find the flux of the vector field F across σ in the direction of positive orientation. F( x , y , z ) = x i + y j + z k; σ is the portion of the sphere r ( u , v ) = 2 sin u cos v i + 2 sin u sin v j + 2cos u k with 0 ≤ u ≤ π / 3 , 0 ≤ v ≤ 2 π .
Find the flux of the vector field F across
σ
in the direction of positive orientation.
Find the flux of the vector field F across
σ
in the direction of positive orientation.
F(
x
,
y
,
z
)
=
x
i
+
y
j
+
z
k;
σ
is the portion of the sphere
r
(
u
,
v
)
=
2
sin
u
cos
v
i
+
2
sin
u
sin
v
j
+
2cos
u
k
with
0
≤
u
≤
π
/
3
,
0
≤
v
≤
2
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.
Let u = 2i - j, v = 4i + j, and w = i + 5j. Find specified scalar u . v + u . w.
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
Precalculus: Mathematics for Calculus (Standalone Book)
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