Vector Addition? Which Vectors Do I Draw and Where?

AI Thread Summary
To solve the vector addition problem involving vectors a and b with magnitudes of 2 and 3 at a 50-degree angle, the cosine and sine laws are essential for determining the resultant vector. The calculated magnitude of the resultant vector 5a - 2b is 7.67, but confusion arises regarding the correct direction and angle due to the choice of vector representation. A recommended approach is to select one vector as the x-axis and decompose the other vector into its components for accurate addition. This method helps clarify the resultant direction and angle, ensuring consistency in the calculations. Proper vector drawing and component analysis are crucial for achieving the correct results in vector addition problems.
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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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