Find the magnitude and direction of `r_(1)-r_(2)` when `|r_(1)|=5` and points North-East while `|r_(2)|=5` but points North-West.

Answer

`5sqrt(5)`, west to east

Explanation

Here, `r_(1)=OA` pointing nort-east and `r_(2)=OB` pointing north-west. Where |OA|=|OB|=5.
as shown in figure.

`therefore angle BOA=90` (using triangle law)
Clearly, `angleBOA` is right angled at O.
`thereforeBA^(2)=OA^(2)+OB^(2)+5^(2)+5^(2)=50`
`implies|BA|=5sqrt(5)`
or `|r_(1)-r_(2)|=5sqrt(5)`.
i.e., `r_(1)-r_(2)` has magnitude `5sqrt(5)` and points from west to east.