Given an Electric Field find the necessary Work to move a charge Q

[kacete]

Homework Statement

Given the Electric field $$\vec{E}=z\vec{u_{x}}-3y^{2}\vec{u_{y}}+x\vec{u_{z}} V/m$$ find the necessary Work to move a charge $$Q=7\mu C$$ along an incremental path of $$1mm$$ distance in the direction of $$2\vec{u_{x}}-6\vec{u_{y}}-3\vec{u_{z}}$$ which locates in $$P(1,2,3)$$

Homework Equations

Work
$$W=-Q\int^{f}_{i}\vec{E}.d\vec{l}$$
i - inicial point
f - final point
Solution
$$W=-75nJ$$

The Attempt at a Solution

Converting to base units
$$Q=7\mu C=7x10^{-6}C$$
$$d=1mm=1x10^{-3}m$$
The electric field at the given point
$$\vec{E}=3\vec{u_{x}}-12\vec{u_{y}}+1\vec{u_{z}} V/m$$
The equation
$$W=-Q\int^{f}_{i}\vec{E}.d\vec{l}=-Q.E\int^{f}_{i}dl.(2\vec{u_{x}}-6\vec{u_{y}}-3\vec{u_{z}})$$
where $$\int^{f}_{i}dl=1x10^{-3}$$
My solution
$$W=-525nJ$$

Where did I go wrong?

 

[Phyisab****]

You need to make dl a unit vector.

 

[kacete]

Can't believe it was that simple. I'm embarrassed. Thank you!