Ok....

I am asked how a vector's

From mathworld:

If you and I see a car drive east at 50 Km/h and you are standing at what you call the origin, and I am standing lets say 5m along what you are calling the positive y-axis, and I call my point the origin with my basis vectors being parrallel to your basis vectors, then do we both give the same components to describe the vector for the car?

To me it seems like this should not always be the case. After all, one position vector has different components then another, right? If we just shift these around by translation, but keep the same direction, then haven't we changed the magnitude from one coordinate system to the next?

I am asked how a vector's

__components__transform under a**translation**of coordinates.From mathworld:

Does that imply that the components used to describe the vector remain unchanged?Since vectors remain unchanged under translation, it is often convenient to consider the tail A as located at the origin when, for example, defining vector addition and scalar multiplication.

If you and I see a car drive east at 50 Km/h and you are standing at what you call the origin, and I am standing lets say 5m along what you are calling the positive y-axis, and I call my point the origin with my basis vectors being parrallel to your basis vectors, then do we both give the same components to describe the vector for the car?

To me it seems like this should not always be the case. After all, one position vector has different components then another, right? If we just shift these around by translation, but keep the same direction, then haven't we changed the magnitude from one coordinate system to the next?

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