Register to reply

Dot product of vector and del.

by pyroknife
Tags: product, vector
Share this thread:
pyroknife
#1
Feb8-14, 02:14 PM
P: 398
I'm not sure which section is best to post this question in.

I was wondering if the expression (u $ ∇) is the same as (∇ $ u).
Here $ represents the dot product (I couldn't find this symbol.
∇=del, the vector differentiation operator
and u is the velocity vector or any other vector
Phys.Org News Partner Mathematics news on Phys.org
'Moral victories' might spare you from losing again
Fair cake cutting gets its own algorithm
Effort to model Facebook yields key to famous math problem (and a prize)
lurflurf
#2
Feb8-14, 03:05 PM
HW Helper
P: 2,263
The usual convention is that ∇ acts to the right so (u $ ∇) and (∇ $ u) are not equal.

This is analogous to asking if uD is equal to D u where D is the differentiation operator.
HallsofIvy
#3
Feb8-14, 05:40 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,340
QUOTE=pyroknife;4654871]I'm not sure which section is best to post this question in.

I was wondering if the expression (u $ ∇) is the same as (∇ $ u).
Here $ represents the dot product (I couldn't find this symbol.
∇=del, the vector differentiation operator
and u is the velocity vector or any other vector[/QUOTE]
Before anyone can answer that question, you will have to tell us what you mean by "(u $ ∇). The reason I say that is that things like [itex]\nabla\cdot u[/itex] and [itex]\nabla\times u[/itex] are mnemonics for [itex]\partial u_x/\partial x+ \partial u_y/\partial y+ \partial u_z/\partial [/itex] and [itex](\partial u_z/\partial y- \partial u_y/\partial z)\vec{i}+ (\partial u_x/\partial z- \partial u_z/\partial x)\vec{j}+ (\partial u_y/\partial x- \partial u_x/\partial y)\vec{k}[/itex]. In particular "[itex]\nabla[/itex]" is NOT a real vector and you cannot combine it with vector functions without saying HOW that is to be done.


Register to reply

Related Discussions
Dot product of a vector with the derivative of its unit vector Calculus & Beyond Homework 7
Ev(Unit Vector) and projection of a vector in a dot product Calculus 1
Vector product VS dot product in matrix Linear & Abstract Algebra 6
Vector Algebra - Vector Triple Product Proof Calculus & Beyond Homework 14
Vector product - operator's a vector? Differential Equations 7