Question

The magnitude of a negative of a vector is negative. O True O False

Answer 1

Answer:

The given statement is false.

Explanation:

For any negative vector

$\overrightarrow{r}=-x\widehat{i}-y\widehat{j}$

The magnitude of the vector is given by

$|r|=\sqrt{(-x)^{2}+(-y)^{2}}\\\\|r|=\sqrt{x^2+y^2}$

As we know that square root of any quantity cannot be negative thus we conclude that the right hand term in the above expression cannot be negative hence we conclude that magnitude of any vector cannot be negative.