Finding direction after adding/subtracting vectors?

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SUMMARY

The discussion focuses on vector addition and subtraction, specifically addressing the calculation of the resultant vector direction after performing operations on vectors A and B. The user correctly identifies the magnitude of the resultant vector as 117 but struggles with determining the correct angle, initially calculating it as 71.8 degrees. The key takeaway is the necessity of adjusting the angle by subtracting from 180 degrees when the resultant vector lies in the second or third quadrant, which is clarified through a sketch of the vectors involved.

PREREQUISITES
  • Understanding of vector addition and subtraction
  • Familiarity with trigonometric functions, specifically tangent and inverse tangent
  • Knowledge of vector components (rx and ry)
  • Ability to interpret vector diagrams
NEXT STEPS
  • Study vector component calculations in detail
  • Learn about vector direction adjustments based on quadrant placement
  • Explore graphical methods for vector addition and subtraction
  • Practice problems involving angles and magnitudes of resultant vectors
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This discussion is beneficial for physics students, educators, and anyone seeking to enhance their understanding of vector operations in two-dimensional space.

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Homework Statement



For the vectors given in Fig. 3-32 (|A| = 67.0 and θ = 55.5°), determine the following.

Image for the problem (http://www.webassign.net/giancoli5/3_35alt.gif)

Need to find:

C-A-B

Direction (counterclockwise from the +x axis is positive)



Homework Equations






The Attempt at a Solution




I understand how to find magnitude when adding and subtracting vectors. And I understand that the angle is found by tan^-1 (ry/rx). I got 117 for the magnitude. My rx is -36.5 and my ry is -111.22. So I took the inverse tangent and got 71.8, which is incorrect. I know that sometimes you have to subtract that angle from 180 or something, but I honestly don't know why or when you do that.

If anyone can explain this to me, I would greatly appreciate it!
 
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Make a rough sketch of C + (-A) + (-B) to give you an idea of whether you need to add or subtract 180° .
 

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