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!