Solved: R Vectors in Different Drawings Same Magnitude?

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The resultant vector of A + B - C maintains the same magnitude regardless of the arrangement in different drawings. This is due to the commutative property of vector addition, which allows the order of addition to be rearranged without affecting the result. By assigning numerical values to the vectors, one can easily verify this consistency. The discussion confirms that the resultant remains unchanged despite the visual differences in representation. Understanding vector addition principles is crucial for accurate calculations in physics and engineering contexts.
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[SOLVED] Is the R the same?

Question : Is the resultant vector of A + B - C the same magnitude in both drawings? I rearranged the vectors to form a different shape, but they would still have the same resultant vector, right?

http://img150.imageshack.us/img150/826/38838600id4.gif
 
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Yes, because essentially what you are doing in the first drawing is A + B + (-C), whereas in the second drawing you have B + (-C) + A.

This is perfectly fine since vector addition is commutative (it doesn't matter what order the vectors are added in).
 
Easy way to check is assign simple numbers to your variables.
 
Thank you for the quick and accurate results.
 

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