Properties of div and curl Prove the following properties of the divergence and curl. Assume F and G are differentiable vector fields and c is a real number. a. ∇ ⋅ ( F + G ) = ∇ ⋅ F + ∇ ⋅ G b. ∇ × ( F + G ) = ( ∇ × F ) + ( ∇ × G ) c. ∇ ⋅ ( c F ) = c ( ∇ ⋅ F ) d. ∇ × ( c F ) = c ( ∇ × F )
Properties of div and curl Prove the following properties of the divergence and curl. Assume F and G are differentiable vector fields and c is a real number. a. ∇ ⋅ ( F + G ) = ∇ ⋅ F + ∇ ⋅ G b. ∇ × ( F + G ) = ( ∇ × F ) + ( ∇ × G ) c. ∇ ⋅ ( c F ) = c ( ∇ ⋅ F ) d. ∇ × ( c F ) = c ( ∇ × F )
Properties of div and curl Prove the following properties of the divergence and curl. Assume F and G are differentiable vector fields and c is a real number.
a.
∇
⋅
(
F
+
G
)
=
∇
⋅
F
+
∇
⋅
G
b.
∇
×
(
F
+
G
)
=
(
∇
×
F
)
+
(
∇
×
G
)
c.
∇
⋅
(
c
F
)
=
c
(
∇
⋅
F
)
d.
∇
×
(
c
F
)
=
c
(
∇
×
F
)
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.
Divergence and Curl of a vector field are
Select one:
a. Scalar & Scalar
b. Non of them
c. Vector & Scalar
d. Vector & Vector
e. Scalar & Vector
A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by
= (x - y, z + y + 9, z) and the net is decribed by the equation y = V1-x - z, y 2 0, and oriented in the positive y-
direction.
(Use symbolic notation and fractions where needed.)
V. dS =
X=r sinø cose
y=r sinø sina
z=r cosø
r² = x² + y² + z²
Determine a,, a, , əz ,ə, ,əg,de
Determine also parallel vector fields.
Chapter 17 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
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