Exercise 4.4.18

$A=a=(1,-1,0,0);B=b-p=\left(\frac{1}{2},\frac{1}{2},-1,0\right);C=c-p_A-p_B=\left(\frac{1}{3},\frac{1}{3},\frac{1}{3},-1\right)$. Notice the pattern in those orthogonal $A,B,C$. In $R^5,D$ would be $\left(\frac{1}{4},\frac{1}{4},\frac{1}{4},\frac{1}{4},-1\right)$. Gram-Schmidt would go on to normalize $q_1=A∕\parallel A\parallel ,q_2=B∕\parallel B\parallel ,q_3=C∕\parallel C\parallel$.