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I noticed vectors are usually said to have "length" and "direction", but then it is said that people want to find the "magnitude". Is this just a difference in terminology or is there something more to it?

For example, here they discuss "magnitude" and here they use the word "length".

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1 Answer

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This is just a difference in terminology. This quantity is also called the norm of a vector. If we are thinking of a vector as representing the line segment from the origin to a given point, we may interpret the norm as the length of this line segment. If we are thinking of a vector as representing a physical quantity like acceleration or velocity, we may interpret the norm as the magnitude of this quantity (how "large" it is, regardless of its direction).

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