Identities Prove the following identities. Assume φ is a differentiablescalar-valued function and F and G are differentiable vectorfields, all defined on a region of ℝ3. ∇ (F ⋅ G ) = (G ⋅ ∇) F + (F ⋅ ∇)G + G x (∇ x F) + F x (∇ x G)
Vector Arithmetic
Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.
Vector Calculus
Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.
Identities Prove the following identities. Assume φ is a differentiable
scalar-valued function and F and G are differentiable
fields, all defined on a region of ℝ3.
∇ (F ⋅ G ) = (G ⋅ ∇) F + (F ⋅ ∇)G + G x (∇ x F) + F x (∇ x G)
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