Is the Magnitude of Vector Addition Equal to the Sum of Magnitudes?

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The discussion centers on whether the magnitude of vector addition, |A+B|, is equal to the sum of the magnitudes, |A|+|B|. The consensus is that this is not always true, particularly when vectors have different directions. The directionality of vectors affects their resultant magnitude, leading to different outcomes based on their orientation. An algebraic approach using the dot product is suggested to further understand the relationship between vector magnitudes. Overall, the key takeaway is that vector addition does not simply equate to the sum of magnitudes due to directional influences.
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Homework Statement



Is it always true that |A+B|=|A|+|B|?

The Attempt at a Solution



My quick answer to this question was no. But when i was asked why i really couldn't come up with much.

any help is appreciated!
 
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Well, vector has direction. Thinking of the sum of vectors with different direction combinations ( same direction, different direction), then you will have your answer.
 
For an algebraic approach, consider that |X|2 = X.X (dot product). Square both sides of your equation and apply that.
 

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