DotExpand[exp] expands dot products in
exp.
Overview, DOT, DotSimplify, DeclareNonCommutative, UnDeclareNonCommutative
DOT[a x + b y + c z, d + e + f]
DotExpand[%](a x+b y+c z).(d+e+f)
a d x+a e x+a f x+b d y+b e y+b f y+c d z+c e z+c f z
DeclareNonCommutative /@ {a, b, c, d, e, f};
DotExpand[DOT[a x + b y + c z, d + e + f]]x a.d+x a.e+x a.f+y b.d+y b.e+y b.f+z c.d+z c.e+z c.f
UnDeclareNonCommutative /@ {a, b, c, d, e, f};
DotExpand[DOT[a x + b y + c z, d + e + f]]a d x+a e x+a f x+b d y+b e y+b f y+c d z+c e z+c f z