# Finding net force on a charge (direction help)

## Homework Statement

In a region of two-dimensional space, there are three fixed charges: +1 mC at (0, 0), −2 mC at (12 mm, -7 mm), and +3 mC at (-6 mm, 18 mm). What is the net force on the −2-mC charge?
magnitude
direction ° counterclockwise from the +x-axis

## The Attempt at a Solution

So to solve I translated the axes so the origin would be at the -2 mC charge.

1 mC at (-12,7), 3 mC at (-18,25)

E = kq1q2/r2 is a vector along the line joining the two charges.

For the first charge, E =

(8.99 * 109 Nm2/C2)(1 * 10-3 C)(2 * 10-3 C)/((12 * 10-3 m)2 + (7 * 10-3 m)2) = 9.31 * 107 N/C; in vector form given the signs of the charge and the location, E = -8.04 * 107i + 4.69 * 107j N/C

For the second charge, E =

(8.99 * 109 Nm2/C2)(3 * 10-3 C)(2 * 10-3 C)/((18 * 10-3 m)2 + (25 * 10-3 m)2) = 5.68 * 107 N/C; in vector form given the signs of the charge and the location, E = -3.32 * 107i + 4.61 * 107j N/C

Combining components, Etotal = -1.137 * 108i + 9.30 * 107j N/C

magnitude = 1.469 * 108 N/C

direction = 140.7°

My problem is the direction, I check my work and did it again but when I enter it into my homework it says it's wrong. Am I misunderstanding the counterclockwise from the +x-axis or can someone help me out please.