## Linear Algebra: A Modern Introduction

The model situation in plane $\mathbb{R}^2$ $Unit \;vectotrs\; is\; \overrightarrow{a}\;=(1,0)\; from\;East\;\;\;\;\;\;\;and\;\;\;\;\;\;\overrightarrow{b}\;=(0,-1)\;from\;North\\\\$ When wind blows: $200\;\overrightarrow{a}\;+\;40\;\overrightarrow{b}\;$ $=\;200(1,0)\;+\;40(0,-1)\;=\;(200,0)\;+\;(0,-40)\;=\;(200,-40)\\\\$ The velocity of the plane: $\left \| 200\;\overrightarrow{a}\;+\;40\;\overrightarrow{b} \right \|\;=\;\sqrt{200^2\;+\;(-40)^2}\;=\;203.96\\\\$ Resultant velocity of the airplane is 203.96 miles per hour.