Identities Prove the following identities. Assume that φ is a differentiable scalar-valued function and F and G are differentiable vector fields, all defined on a region of R 3 . 68. ∇ × ( φ F ) = ( ∇ φ × F ) + ( φ ∇ × F ) (Product Rule)
Identities Prove the following identities. Assume that φ is a differentiable scalar-valued function and F and G are differentiable vector fields, all defined on a region of R 3 . 68. ∇ × ( φ F ) = ( ∇ φ × F ) + ( φ ∇ × F ) (Product Rule)
IdentitiesProve the following identities. Assume that φ is a differentiable scalar-valued function andFandGare differentiable vector fields, all defined on a region of R3.
68.
∇
×
(
φ
F
)
=
(
∇
φ
×
F
)
+
(
φ
∇
×
F
)
(Product Rule)
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.
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)
only solute question c , please
Please use similar notation from the images, hope they help, thank you.
Let V be an n-dimensional vector space. Define f : V \rightarrow \R by f(v) = |v2|. Let p,q \in V. Find dfp(q).
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