Answer to Question #121128 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

As per the question,

Let the vector is $\overrightarrow{r}=a \hat{i}+b\hat{j}+c\hat{k}$

1) As per the statement, if one component a=0, then magnitude of the vector $|\overrightarrow{r}|=\sqrt{0^2+b^2+c^2}=\sqrt{b^2+c^2}$

Hence statement 1 is incorrect.

2) it is not possible to add vector quantity to scalar quantity.

3) If two vectors have unequal in magnitude then it is not possible to get zero by adding them.

4) Statement 4 is incorrect.  The magnitude of a vector may be positive even if all of its components are negative.

5) from the first solution, we can say that magnitude of the vector is independent of the coordinate system used hence statement 5 is correct.