Vector Addition? Which Vectors Do I Draw and Where?

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SUMMARY

The discussion focuses on solving the vector equation 5a - 2b, where vectors a and b have magnitudes of 2 and 3, respectively, and an angle of 50 degrees between them. The correct magnitude calculated using the Cosine Law is 7.67. However, participants express confusion regarding the direction and angle of the resultant vector due to varying drawing methods. The recommended approach is to establish one vector as the x-axis and decompose the other vector into its components for accurate addition.

PREREQUISITES
  • Understanding of vector magnitudes and directions
  • Familiarity with the Cosine Law and Sine Law
  • Ability to perform vector component breakdown
  • Basic knowledge of trigonometric functions
NEXT STEPS
  • Learn how to apply the Cosine Law in vector addition
  • Study vector component decomposition techniques
  • Explore graphical methods for vector representation
  • Investigate the Sine Law for solving triangles in vector problems
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Students studying physics or mathematics, particularly those focusing on vector analysis and problem-solving in geometry.

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Homework Statement


Vectors a and b have magnitudes 2 and 3. The angle between them is 50 degrees. Determine 5a - 2b and determine its magnitude and direction


Homework Equations


Cosine Law and Sine Law



The Attempt at a Solution


I can solve for the magnitude using the cos law and obtain an answer of 7.67 which is correct, however the direction and angle looks as if which vector i draw and where I draw it Heres a picture (The magnitudes I have just labelled as 10 which is 5a and 6 for 2b) :

Untitled_zpsd4cc7bd5.png


Which drawing should I use, because It results in me getting different angles and direction
 
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The most straightforward approach would be to pick one vector as the x axis, then break the other into its component, and add them that way.
 

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