Where am I going wrong with this vector addition?

AI Thread Summary
The discussion centers on confusion regarding vector addition in the context of forces from electric charges. The user is calculating the sum of two force vectors, F13 and F23, but arrives at a negative result, while the book states a positive value. The specific values mentioned are F13 as -1.35*10^-3 j and F23 as 9.67*10^-4 j, leading to a discrepancy in the final result. There is speculation that a typographical error in the book may have contributed to the misunderstanding, particularly regarding the placement of the negative sign. Clarification on vector addition principles and potential errors in the book's answer is sought.
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Homework Statement
Three charged particles with q1 = -50 nC, q2 = +50 nC, and q3 = +30 nC are placed on the corners of the 5.0 cm X 10.0 cm rectangle shown in Figure 22.18lkl. What is the net force on charge q3 due to the other two charges? Give your answer both in component form and as a
magnitude and direction
Relevant Equations
F=kq1q2/r^2
I am following along with an example in my book regarding force from an electric charge. I understand the process but I believe I am getting something wrong when it comes to adding the vectors.

Essentially, F13 is equal to -1.35*10^-3 j and when I add that to the j component of F23 which is 9.67*10^-4 J I am getting -3.84*10^-4. The book is giving positive 3.84*10^-4. I have highlighted the values in the PDF attached. Could someone help me understand why it would be positive?
 

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Clearly a typo in the given answer.
Maybe the minus sign on the i coefficient was supposed to be outside the parentheses.
 
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