## Linear Algebra: A Modern Introduction

The model situation in plane $\mathbb{R}^2$ $Unit \;vectotrs\; is\; \overrightarrow{a}\;=(0,1)\; from\;North\;\;\;\;\;\;\;and\;\;\;\;\;\;\overrightarrow{b}\;=(1,0)\;from\;East\\\\$ When wind blows: $4\;\overrightarrow{a}\;+\;3\;\overrightarrow{b}\;=\;4(0,1)\;+\;3(1,0)\;=\;(0,4)\;+\;(3,0)\;=\;(3,4)\\\\$ The velocity of the plane: $\left \| 4\;\overrightarrow{a}\;+\;3\;\overrightarrow{b} \right \|\;=\;\sqrt{3^2\;+\;4^2}\;=\;5\\\\$ Resultant velocity of the boat is 5 miles per hour.