Hello, Solid8Snake!
A plane goes from city A to city B. In a Cartesian plane.
City A is at the origin and city B has coordinates (100,150).
If there is no wind, the flight lasts one hour. Unfortunately, there is a wind.
If the pilot does not adjust his flight path, he will be at point (120,160) after an hour.
What is the speed of the wind? Code:
 C
 o(120,160)
 * *
 * *
 * *
 * *
 * *
 * o(100,150)
 * * B
 * *
 * *
A *                   

The plane's original vector was: .$\displaystyle \overrightarrow{AB} \:=\:\langle100,150\rangle$
Due to the wind, $\displaystyle \overrightarrow{BC} \:=\:\langle x,y\rangle$, it flies to $\displaystyle C(120,160).$
Since $\displaystyle \overrightarrow{AB} + \overrightarrow{BC} \:=\:\overrightarrow{AC}$, we have: .$\displaystyle \langle 100,150\rangle + \langle x,y\rangle \:=\:\langle120,160\rangle$
. . Hence: .$\displaystyle \begin{array}{ccccccc}100 + x \:=\:120 & \Longrightarrow & x \:=\:20 \\ 150 + y \:=\:160 & \Longrightarrow & y \:=\:10 \end{array}$
The wind's vector is: .$\displaystyle \overrightarrow{BC} \:=\:\langle 20,10\rangle$
Its speed (magnitude) is: .$\displaystyle \overrightarrow{BC} \;=\;\sqrt{20^2+10^2} \;=\;\sqrt{500} \;=\;10\sqrt{5}$