Exercise 4.4.16

$p=\left(a^{T}b∕a^{T}a\right)a=14a∕49=2a∕7$ is the projection of $b$ onto $a.q_1=a∕\parallel a\parallel =$ $a∕7$ is $(4,5,2,2)∕7.B=b-p=(-1,4,-4,-4)∕7$ has $\parallel B\parallel =1$ so $q_2=B$.