How Does the Dot Product Interact with the Gradient in Vector Calculus?

[Brown Arrow]

dot product, and the gradient urgent pls!...

Homework Statement

Δ<-- this be the gradient and B<-- be a vector B X= xi +yj + zk
*<---- be the dot product.
(B*Δ)X=B

Homework Equations

n/a

The Attempt at a Solution

im not sure how to go about this but this is what i did

i did Δ*B so i got B_x + B_y + B_z
then its multiplyed by X :/ not making any sense to me

help pls
BA

 

[Brown Arrow]

any one ? :/

 

[dextercioby]

So you're trying to show that

$$(\mathbf{B}\cdot\nabla)\mathbf{X} = \mathbf{B}$$.

Well the scalar product in the brackets is a differential operator. What's its form ?

 

[hunt_mat]

To expand on what bigubau said:
$$\mathbf{B}\cdot\nabla =B_{x}\frac{\partial}{\partial x}+B_{y}\frac{\partial}{\partial y}+B_{z}\frac{\partial}{\partial z}$$
This is applied to each of the components of X, so for example:
$$(\mathbf{B}\cdot\nabla )\mathbf{X}|_{x}=B_{x}\frac{\partial X_{x}}{\partial x}+B_{y}\frac{\partial X_{x}}{\partial y}+B_{z}\frac{\partial X_{x}}{\partial z}$$