Verify answers for normal factorization problem. 2.16

<< CliffordBasic`;
$SetSignature={3,0};

a = -(e[2] - e[3])
b = e[1] - e[2]/2 - e[3]/2

(*InnerProduct[a,b]
OuterProduct[a,b]*)
GeometricProduct[a,b]

c = e[1] - e[3]
d = e[2] - e[3]
cp = c - InnerProduct[c,d] d/InnerProduct[d,d]// Simplify

(*InnerProduct[c,d]
OuterProduct[c, d]*)
(*InnerProduct[cp,d]
OuterProduct[cp, d]*)
GeometricProduct[cp, d]

m = e[1] +e[2] - 2 e[3]
n = (e[2] - e[1])/2

GeometricProduct[ m, n ]