Understanding Vector Magnitude and Components: Common Questions Answered

[eraemia]

Homework Statement

I have two questions on vectors:
1) Does the magnitude of a vector vary depending on how one chooses a reference frame?
2) Can a component of a vector be negative?

Homework Equations

n/a

The Attempt at a Solution

1) No, because regardless of the reference frame, the magnitude is always the same?
2) Yes, say if the vector points -y or -x or -z

 

[rootX]

1) is wrong, I think.

because what if frame of reference is also moving at the velocity of v, where v is the velocity of the object being observed?..

 

[eraemia]

Yeah, that makes sense. But doesn't the vector remain the same? For example, if I have a vector of 5m/s north, it remains that vector whether or not the reference frame is stationery Earth or a train moving at 10m/s north... Or is the question asking like the magnitude of the object and not the vector? Sorry, I'm confusing.

 

[rootX]

I am not sure if they are asking for resultant vector, or that original vector... (refer to those relatve motion questions)
mag. of the resultant != mag of org

yea, otherwise org. vectors remains that same vector unless some force is applied to it..