Understanding the Del Operator in Vector Calculus

[namnimnom]

F is a vector from origin to point (x,y,z) and û is a unit vector.
how to prove?
(û⋅∇)F=û

only tried expanding but it's going nowhere

 

[blue_leaf77]

If $\hat u = u_x \hat x + u_y \hat y + u_z \hat z$, then you have
$$
\hat u \cdot \nabla = u_x \partial_x + u_y \partial_y + u_z \partial_z
$$
which is a scalar operator. With $\mathbf F = x \hat x + y \hat y + z \hat z$, I don't see why it's difficult to evaluate $(\hat u \cdot \nabla) \mathbf F$.

 

[BvU]

Hello nnn,

only tried expanding but

This does not help us to help you effectively. In such a case you should write down your expansion so we can provide better assistance to overcome the hurdle you are experiencing. Or did it help you to read that it isn't difficult ?

 

[namnimnom]

If $\hat u = u_x \hat x + u_y \hat y + u_z \hat z$, then you have
$$
\hat u \cdot \nabla = u_x \partial_x + u_y \partial_y + u_z \partial_z
$$
which is a scalar operator. With $\mathbf F = x \hat x + y \hat y + z \hat z$, I don't see why it's difficult to evaluate $(\hat u \cdot \nabla) \mathbf F$.

Hello nnn,
This does not help us to help you effectively. In such a case you should write down your expansion so we can provide better assistance to overcome the hurdle you are experiencing. Or did it help you to read that it isn't difficult ?

solved it. I'm probably TOO new to this hahahha thank you! :)