Answer to Question #118107 in Classical Mechanics for Lizwi

Question

Which of the following is an accurate statement?
1 : The magnitude of a vector can be zero even though one of its components is not zero.
2 : It is possible to add a scalar quantity to a vector.
3 : Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero.
4 : Rotating a vector about an axis passing through the tip of the vector does not change the vector.
5 : The magnitude of a vector is independent of the coordinate system used.

Answer 1

The correct statement will be the fifth statement i.e "The magnitude of a vector is independent of the coordinate system used."

Reason:

Lets draw a vector $\overrightarrow{AB}$ with different coordinate system below,

Now, if we consider the vector $\overrightarrow{AB}$ with coordinate system $D,C \: \&E$ , clearly from the above picture ,coordinates of $A \: \& B$ are different with respect to system $D,C,E$ but the magnitude of $\overrightarrow{AB}$

i.e $||\overrightarrow{AB}||$ is remains same(doesn't change).