2819.sagews

var('t')
A=vector([1,3])
B=vector([-3,2])
D=(B-A)
ab=A+t*D

ab.subs(t==0)

(1, 3)

var('s')
Dn=vector([-D[1],D[0]])
nab0=s*Dn

S=solve([ab[0]==nab0[0],ab[1]==nab0[1]],t,s)[0]
ab.subs(S[0]),nab0.subs(S[1])

((-11/17, 44/17), (-11/17, 44/17))