Exercise 4.3.6

$a=(1,1,1,1)$ and $b=(0,8,8,20)$ give $\hat{x}=a^{T}b∕a^{T}a=9$ and the projection is $\hat{x}a=p=(9,9,9,9)$. Then $e^{T}a={(-9,-1,-1,11)}^T(1,1,1,1)=0$ and the shortest distance from $b$ to the line through $a$ is $\parallel e\parallel =\sqrt{204}$.