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.
Let F and G be vector fields with differentiable components. Express
curl (F x G) in term of div and dot products.
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)
Sketch the vector fields. Use a table for it.
F(x,y)=<x,y-x>
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.