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 differentiablevector 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
(
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)
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
Properties of div and curl Prove the following properties of thedivergence and curl. Assume F and G are differentiable vectorfields and c is a real number.a. ∇ ⋅ (F + G) = ∇ ⋅ F + ∇ ⋅ Gb. ∇ x (F + G) = (∇ x F) + (∇ x G)c. ∇ ⋅ (cF) = c(∇ ⋅ F)d. ∇ x (cF) = c(∇ ⋅ F)
Let F and G be vector fields with differentiable components. Express
curl (F x G) in term of div and dot products.
Chapter 17 Solutions
Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
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