Question

If a vector pointing upward has a positive magnitude, a vector pointing downward has a negative magnitude. True or false?

Answer 1

The statement is false.

Explanation:

For any vector 'r' we have

`\overrightarrow{r}=x\widehat{i}+y\widehat{j}+z\widehat{k}`

The magnitude is given by

`|r|=\sqrt{x^(2)+y^(2)+z^(2)}..........(i)`

As we know that the upon squaring a term the result is always positive thus the term in right side of equation i is always positive no matter weather the terms (x,y,z) are positive or negative hence we conclude that magnitude of any vectorial quantity is always positive irrespective of it's direction.